TSTP Solution File: NUM424+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM424+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:09:37 EDT 2022
% Result : Theorem 189.44s 119.23s
% Output : Proof 189.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM424+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 10:21:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 189.44/119.23 % SZS status Theorem
% 189.44/119.23 % SZS output start Proof
% 189.44/119.23 tff(sdtpldt0_type, type, (
% 189.44/119.23 sdtpldt0: ( $i * $i ) > $i)).
% 189.44/119.23 tff(smndt0_type, type, (
% 189.44/119.23 smndt0: $i > $i)).
% 189.44/119.23 tff(xa_type, type, (
% 189.44/119.23 xa: $i)).
% 189.44/119.23 tff(xb_type, type, (
% 189.44/119.23 xb: $i)).
% 189.44/119.23 tff(sdtasdt0_type, type, (
% 189.44/119.23 sdtasdt0: ( $i * $i ) > $i)).
% 189.44/119.23 tff(tptp_fun_W0_1_type, type, (
% 189.44/119.23 tptp_fun_W0_1: $i)).
% 189.44/119.23 tff(xq_type, type, (
% 189.44/119.23 xq: $i)).
% 189.44/119.23 tff(sz00_type, type, (
% 189.44/119.23 sz00: $i)).
% 189.44/119.23 tff(aInteger0_type, type, (
% 189.44/119.23 aInteger0: $i > $o)).
% 189.44/119.23 tff(sz10_type, type, (
% 189.44/119.23 sz10: $i)).
% 189.44/119.23 tff(sdteqdtlpzmzozddtrp0_type, type, (
% 189.44/119.23 sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o)).
% 189.44/119.23 tff(aDivisorOf0_type, type, (
% 189.44/119.23 aDivisorOf0: ( $i * $i ) > $o)).
% 189.44/119.23 tff(1,plain,
% 189.44/119.23 (aInteger0(xa) <=> aInteger0(xa)),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(2,axiom,(((aInteger0(xa) & aInteger0(xb)) & aInteger0(xq)) & (~(xq = sz00))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__704')).
% 189.44/119.23 tff(3,plain,
% 189.44/119.23 ((aInteger0(xa) & aInteger0(xb)) & aInteger0(xq)),
% 189.44/119.23 inference(and_elim,[status(thm)],[2])).
% 189.44/119.23 tff(4,plain,
% 189.44/119.23 (aInteger0(xa) & aInteger0(xb)),
% 189.44/119.23 inference(and_elim,[status(thm)],[3])).
% 189.44/119.23 tff(5,plain,
% 189.44/119.23 (aInteger0(xa)),
% 189.44/119.23 inference(and_elim,[status(thm)],[4])).
% 189.44/119.23 tff(6,plain,
% 189.44/119.23 (aInteger0(xa)),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[5, 1])).
% 189.44/119.23 tff(7,plain,
% 189.44/119.23 (^[W0: $i] : refl((aInteger0(smndt0(W0)) | (~aInteger0(W0))) <=> (aInteger0(smndt0(W0)) | (~aInteger0(W0))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(8,plain,
% 189.44/119.23 (![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0))) <=> ![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[7])).
% 189.44/119.23 tff(9,plain,
% 189.44/119.23 (![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0))) <=> ![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(10,plain,
% 189.44/119.23 (^[W0: $i] : rewrite((aInteger0(W0) => aInteger0(smndt0(W0))) <=> (aInteger0(smndt0(W0)) | (~aInteger0(W0))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(11,plain,
% 189.44/119.23 (![W0: $i] : (aInteger0(W0) => aInteger0(smndt0(W0))) <=> ![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[10])).
% 189.44/119.23 tff(12,axiom,(![W0: $i] : (aInteger0(W0) => aInteger0(smndt0(W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mIntNeg')).
% 189.44/119.23 tff(13,plain,
% 189.44/119.23 (![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[12, 11])).
% 189.44/119.23 tff(14,plain,
% 189.44/119.23 (![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[13, 9])).
% 189.44/119.23 tff(15,plain,(
% 189.44/119.23 ![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(skolemize,[status(sab)],[14])).
% 189.44/119.23 tff(16,plain,
% 189.44/119.23 (![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[15, 8])).
% 189.44/119.23 tff(17,plain,
% 189.44/119.23 (((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(xa)) | (~aInteger0(xa)))) <=> ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(xa)) | (~aInteger0(xa)))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(18,plain,
% 189.44/119.23 ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(xa)) | (~aInteger0(xa)))),
% 189.44/119.23 inference(quant_inst,[status(thm)],[])).
% 189.44/119.23 tff(19,plain,
% 189.44/119.23 ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(xa)) | (~aInteger0(xa))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[18, 17])).
% 189.44/119.23 tff(20,plain,
% 189.44/119.23 (aInteger0(smndt0(xa))),
% 189.44/119.23 inference(unit_resolution,[status(thm)],[19, 16, 6])).
% 189.44/119.23 tff(21,plain,
% 189.44/119.23 (aInteger0(xb) <=> aInteger0(xb)),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(22,plain,
% 189.44/119.23 (aInteger0(xb)),
% 189.44/119.23 inference(and_elim,[status(thm)],[4])).
% 189.44/119.23 tff(23,plain,
% 189.44/119.23 (aInteger0(xb)),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[22, 21])).
% 189.44/119.23 tff(24,plain,
% 189.44/119.23 (^[W0: $i, W1: $i] : refl((aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(25,plain,
% 189.44/119.23 (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[24])).
% 189.44/119.23 tff(26,plain,
% 189.44/119.23 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & aInteger0(W1)) <=> (~((~aInteger0(W1)) | (~aInteger0(W0))))), ((~(aInteger0(W0) & aInteger0(W1))) <=> (~(~((~aInteger0(W1)) | (~aInteger0(W0))))))), rewrite((~(~((~aInteger0(W1)) | (~aInteger0(W0))))) <=> ((~aInteger0(W1)) | (~aInteger0(W0)))), ((~(aInteger0(W0) & aInteger0(W1))) <=> ((~aInteger0(W1)) | (~aInteger0(W0))))), ((aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> (aInteger0(sdtpldt0(W0, W1)) | ((~aInteger0(W1)) | (~aInteger0(W0)))))), rewrite((aInteger0(sdtpldt0(W0, W1)) | ((~aInteger0(W1)) | (~aInteger0(W0)))) <=> (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))), ((aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(27,plain,
% 189.44/119.23 (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[26])).
% 189.44/119.23 tff(28,plain,
% 189.44/119.23 (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(29,plain,
% 189.44/119.23 (^[W0: $i, W1: $i] : rewrite(((aInteger0(W0) & aInteger0(W1)) => aInteger0(sdtpldt0(W0, W1))) <=> (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(30,plain,
% 189.44/119.23 (![W0: $i, W1: $i] : ((aInteger0(W0) & aInteger0(W1)) => aInteger0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[29])).
% 189.44/119.23 tff(31,axiom,(![W0: $i, W1: $i] : ((aInteger0(W0) & aInteger0(W1)) => aInteger0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mIntPlus')).
% 189.44/119.23 tff(32,plain,
% 189.44/119.23 (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[31, 30])).
% 189.44/119.23 tff(33,plain,
% 189.44/119.23 (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[32, 28])).
% 189.44/119.23 tff(34,plain,(
% 189.44/119.23 ![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 189.44/119.23 inference(skolemize,[status(sab)],[33])).
% 189.44/119.23 tff(35,plain,
% 189.44/119.23 (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[34, 27])).
% 189.44/119.23 tff(36,plain,
% 189.44/119.23 (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[35, 25])).
% 189.44/119.23 tff(37,plain,
% 189.44/119.23 (((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | aInteger0(sdtpldt0(xb, smndt0(xa))))) <=> ((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | aInteger0(sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(38,plain,
% 189.44/119.23 ((aInteger0(sdtpldt0(xb, smndt0(xa))) | (~aInteger0(smndt0(xa))) | (~aInteger0(xb))) <=> ((~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | aInteger0(sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(39,plain,
% 189.44/119.23 (((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (aInteger0(sdtpldt0(xb, smndt0(xa))) | (~aInteger0(smndt0(xa))) | (~aInteger0(xb)))) <=> ((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | aInteger0(sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.23 inference(monotonicity,[status(thm)],[38])).
% 189.44/119.23 tff(40,plain,
% 189.44/119.23 (((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (aInteger0(sdtpldt0(xb, smndt0(xa))) | (~aInteger0(smndt0(xa))) | (~aInteger0(xb)))) <=> ((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | aInteger0(sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.23 inference(transitivity,[status(thm)],[39, 37])).
% 189.44/119.23 tff(41,plain,
% 189.44/119.23 ((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (aInteger0(sdtpldt0(xb, smndt0(xa))) | (~aInteger0(smndt0(xa))) | (~aInteger0(xb)))),
% 189.44/119.23 inference(quant_inst,[status(thm)],[])).
% 189.44/119.23 tff(42,plain,
% 189.44/119.23 ((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | aInteger0(sdtpldt0(xb, smndt0(xa)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[41, 40])).
% 189.44/119.23 tff(43,plain,
% 189.44/119.23 (aInteger0(sdtpldt0(xb, smndt0(xa)))),
% 189.44/119.23 inference(unit_resolution,[status(thm)],[42, 36, 23, 20])).
% 189.44/119.23 tff(44,plain,
% 189.44/119.23 (^[W0: $i] : refl(((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(45,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[44])).
% 189.44/119.23 tff(46,plain,
% 189.44/119.23 (^[W0: $i] : rewrite(((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(47,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[46])).
% 189.44/119.23 tff(48,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(49,plain,
% 189.44/119.23 (^[W0: $i] : rewrite((aInteger0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(50,plain,
% 189.44/119.23 (![W0: $i] : (aInteger0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[49])).
% 189.44/119.23 tff(51,axiom,(![W0: $i] : (aInteger0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddZero')).
% 189.44/119.23 tff(52,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[51, 50])).
% 189.44/119.23 tff(53,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[52, 48])).
% 189.44/119.23 tff(54,plain,(
% 189.44/119.23 ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 189.44/119.23 inference(skolemize,[status(sab)],[53])).
% 189.44/119.23 tff(55,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[54, 47])).
% 189.44/119.23 tff(56,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[55, 45])).
% 189.44/119.23 tff(57,plain,
% 189.44/119.23 (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~((~(sdtpldt0(sdtpldt0(xb, smndt0(xa)), sz00) = sdtpldt0(xb, smndt0(xa)))) | (~(sdtpldt0(xb, smndt0(xa)) = sdtpldt0(sz00, sdtpldt0(xb, smndt0(xa))))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~((~(sdtpldt0(sdtpldt0(xb, smndt0(xa)), sz00) = sdtpldt0(xb, smndt0(xa)))) | (~(sdtpldt0(xb, smndt0(xa)) = sdtpldt0(sz00, sdtpldt0(xb, smndt0(xa))))))))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(58,plain,
% 189.44/119.23 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~((~(sdtpldt0(sdtpldt0(xb, smndt0(xa)), sz00) = sdtpldt0(xb, smndt0(xa)))) | (~(sdtpldt0(xb, smndt0(xa)) = sdtpldt0(sz00, sdtpldt0(xb, smndt0(xa))))))))),
% 189.44/119.23 inference(quant_inst,[status(thm)],[])).
% 189.44/119.23 tff(59,plain,
% 189.44/119.23 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~((~(sdtpldt0(sdtpldt0(xb, smndt0(xa)), sz00) = sdtpldt0(xb, smndt0(xa)))) | (~(sdtpldt0(xb, smndt0(xa)) = sdtpldt0(sz00, sdtpldt0(xb, smndt0(xa)))))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[58, 57])).
% 189.44/119.23 tff(60,plain,
% 189.44/119.23 (~((~(sdtpldt0(sdtpldt0(xb, smndt0(xa)), sz00) = sdtpldt0(xb, smndt0(xa)))) | (~(sdtpldt0(xb, smndt0(xa)) = sdtpldt0(sz00, sdtpldt0(xb, smndt0(xa))))))),
% 189.44/119.23 inference(unit_resolution,[status(thm)],[59, 56, 43])).
% 189.44/119.23 tff(61,plain,
% 189.44/119.23 (((~(sdtpldt0(sdtpldt0(xb, smndt0(xa)), sz00) = sdtpldt0(xb, smndt0(xa)))) | (~(sdtpldt0(xb, smndt0(xa)) = sdtpldt0(sz00, sdtpldt0(xb, smndt0(xa)))))) | (sdtpldt0(xb, smndt0(xa)) = sdtpldt0(sz00, sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.23 inference(tautology,[status(thm)],[])).
% 189.44/119.23 tff(62,plain,
% 189.44/119.23 (sdtpldt0(xb, smndt0(xa)) = sdtpldt0(sz00, sdtpldt0(xb, smndt0(xa)))),
% 189.44/119.23 inference(unit_resolution,[status(thm)],[61, 60])).
% 189.44/119.23 tff(63,plain,
% 189.44/119.23 (sdtpldt0(sz00, sdtpldt0(xb, smndt0(xa))) = sdtpldt0(xb, smndt0(xa))),
% 189.44/119.23 inference(symmetry,[status(thm)],[62])).
% 189.44/119.23 tff(64,plain,
% 189.44/119.23 (((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(xb)) | (~aInteger0(xb)))) <=> ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(xb)) | (~aInteger0(xb)))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(65,plain,
% 189.44/119.23 ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(xb)) | (~aInteger0(xb)))),
% 189.44/119.23 inference(quant_inst,[status(thm)],[])).
% 189.44/119.23 tff(66,plain,
% 189.44/119.23 ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(xb)) | (~aInteger0(xb))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[65, 64])).
% 189.44/119.23 tff(67,plain,
% 189.44/119.23 (aInteger0(smndt0(xb))),
% 189.44/119.23 inference(unit_resolution,[status(thm)],[66, 16, 23])).
% 189.44/119.23 tff(68,plain,
% 189.44/119.23 (^[W0: $i] : refl(((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))) <=> ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(69,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[68])).
% 189.44/119.23 tff(70,plain,
% 189.44/119.23 (^[W0: $i] : rewrite(((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(71,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[70])).
% 189.44/119.23 tff(72,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(73,plain,
% 189.44/119.23 (^[W0: $i] : rewrite((aInteger0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(74,plain,
% 189.44/119.23 (![W0: $i] : (aInteger0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[73])).
% 189.44/119.23 tff(75,axiom,(![W0: $i] : (aInteger0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddNeg')).
% 189.44/119.23 tff(76,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[75, 74])).
% 189.44/119.23 tff(77,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[76, 72])).
% 189.44/119.23 tff(78,plain,(
% 189.44/119.23 ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 189.44/119.23 inference(skolemize,[status(sab)],[77])).
% 189.44/119.23 tff(79,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[78, 71])).
% 189.44/119.23 tff(80,plain,
% 189.44/119.23 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[79, 69])).
% 189.44/119.23 tff(81,plain,
% 189.44/119.23 (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aInteger0(smndt0(xb))) | (~((~(sdtpldt0(smndt0(xb), smndt0(smndt0(xb))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aInteger0(smndt0(xb))) | (~((~(sdtpldt0(smndt0(xb), smndt0(smndt0(xb))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)))))))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(82,plain,
% 189.44/119.23 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aInteger0(smndt0(xb))) | (~((~(sdtpldt0(smndt0(xb), smndt0(smndt0(xb))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)))))))),
% 189.44/119.23 inference(quant_inst,[status(thm)],[])).
% 189.44/119.23 tff(83,plain,
% 189.44/119.23 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aInteger0(smndt0(xb))) | (~((~(sdtpldt0(smndt0(xb), smndt0(smndt0(xb))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(smndt0(xb)), smndt0(xb))))))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[82, 81])).
% 189.44/119.23 tff(84,plain,
% 189.44/119.23 (~((~(sdtpldt0(smndt0(xb), smndt0(smndt0(xb))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)))))),
% 189.44/119.23 inference(unit_resolution,[status(thm)],[83, 80, 67])).
% 189.44/119.23 tff(85,plain,
% 189.44/119.23 (((~(sdtpldt0(smndt0(xb), smndt0(smndt0(xb))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(smndt0(xb)), smndt0(xb))))) | (sz00 = sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)))),
% 189.44/119.23 inference(tautology,[status(thm)],[])).
% 189.44/119.23 tff(86,plain,
% 189.44/119.23 (sz00 = sdtpldt0(smndt0(smndt0(xb)), smndt0(xb))),
% 189.44/119.23 inference(unit_resolution,[status(thm)],[85, 84])).
% 189.44/119.23 tff(87,plain,
% 189.44/119.23 (sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)) = sz00),
% 189.44/119.23 inference(symmetry,[status(thm)],[86])).
% 189.44/119.23 tff(88,plain,
% 189.44/119.23 (sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sz00, sdtpldt0(xb, smndt0(xa)))),
% 189.44/119.23 inference(monotonicity,[status(thm)],[87])).
% 189.44/119.23 tff(89,plain,
% 189.44/119.23 (((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(smndt0(xb))) | (~aInteger0(smndt0(xb))))) <=> ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(smndt0(xb))) | (~aInteger0(smndt0(xb))))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(90,plain,
% 189.44/119.23 ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(smndt0(xb))) | (~aInteger0(smndt0(xb))))),
% 189.44/119.23 inference(quant_inst,[status(thm)],[])).
% 189.44/119.23 tff(91,plain,
% 189.44/119.23 ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(smndt0(xb))) | (~aInteger0(smndt0(xb)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[90, 89])).
% 189.44/119.23 tff(92,plain,
% 189.44/119.23 (aInteger0(smndt0(smndt0(xb)))),
% 189.44/119.23 inference(unit_resolution,[status(thm)],[91, 16, 67])).
% 189.44/119.23 tff(93,plain,
% 189.44/119.23 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(94,plain,
% 189.44/119.23 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[93])).
% 189.44/119.23 tff(95,plain,
% 189.44/119.23 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) <=> (~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))), ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) <=> (~(~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))))), rewrite((~(~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))), ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))), (((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> (((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))))), rewrite((((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))), (((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(96,plain,
% 189.44/119.23 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[95])).
% 189.44/119.23 tff(97,plain,
% 189.44/119.23 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(98,plain,
% 189.44/119.23 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) <=> (aInteger0(W0) & aInteger0(W1) & aInteger0(W2))), ((((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))))), rewrite(((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))), ((((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))))),
% 189.44/119.23 inference(bind,[status(th)],[])).
% 189.44/119.23 tff(99,plain,
% 189.44/119.23 (![W0: $i, W1: $i, W2: $i] : (((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))),
% 189.44/119.23 inference(quant_intro,[status(thm)],[98])).
% 189.44/119.23 tff(100,axiom,(![W0: $i, W1: $i, W2: $i] : (((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddAsso')).
% 189.44/119.23 tff(101,plain,
% 189.44/119.23 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[100, 99])).
% 189.44/119.23 tff(102,plain,
% 189.44/119.23 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[101, 97])).
% 189.44/119.23 tff(103,plain,(
% 189.44/119.23 ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))),
% 189.44/119.23 inference(skolemize,[status(sab)],[102])).
% 189.44/119.23 tff(104,plain,
% 189.44/119.23 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[103, 96])).
% 189.44/119.23 tff(105,plain,
% 189.44/119.23 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.23 inference(modus_ponens,[status(thm)],[104, 94])).
% 189.44/119.23 tff(106,plain,
% 189.44/119.23 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(smndt0(xb))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(smndt0(smndt0(xb)))) | (sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(smndt0(xb))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(smndt0(smndt0(xb)))) | (sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(107,plain,
% 189.44/119.23 (((sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(smndt0(xb))) | (~aInteger0(smndt0(smndt0(xb))))) <=> ((~aInteger0(smndt0(xb))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(smndt0(smndt0(xb)))) | (sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.23 inference(rewrite,[status(thm)],[])).
% 189.44/119.23 tff(108,plain,
% 189.44/119.23 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(smndt0(xb))) | (~aInteger0(smndt0(smndt0(xb)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(smndt0(xb))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(smndt0(smndt0(xb)))) | (sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa))))))),
% 189.44/119.24 inference(monotonicity,[status(thm)],[107])).
% 189.44/119.24 tff(109,plain,
% 189.44/119.24 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(smndt0(xb))) | (~aInteger0(smndt0(smndt0(xb)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(smndt0(xb))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(smndt0(smndt0(xb)))) | (sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.24 inference(transitivity,[status(thm)],[108, 106])).
% 189.44/119.24 tff(110,plain,
% 189.44/119.24 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(smndt0(xb))) | (~aInteger0(smndt0(smndt0(xb)))))),
% 189.44/119.24 inference(quant_inst,[status(thm)],[])).
% 189.44/119.24 tff(111,plain,
% 189.44/119.24 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(smndt0(xb))) | (~aInteger0(sdtpldt0(xb, smndt0(xa)))) | (~aInteger0(smndt0(smndt0(xb)))) | (sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[110, 109])).
% 189.44/119.24 tff(112,plain,
% 189.44/119.24 ((~aInteger0(smndt0(smndt0(xb)))) | (sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[111, 105, 67, 43])).
% 189.44/119.24 tff(113,plain,
% 189.44/119.24 (sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)), smndt0(xb)), sdtpldt0(xb, smndt0(xa)))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[112, 92])).
% 189.44/119.24 tff(114,plain,
% 189.44/119.24 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | (~aInteger0(smndt0(xb))) | (sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | (~aInteger0(smndt0(xb))) | (sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(115,plain,
% 189.44/119.24 (((sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa))) | (~aInteger0(smndt0(xa))) | (~aInteger0(xb)) | (~aInteger0(smndt0(xb)))) <=> ((~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | (~aInteger0(smndt0(xb))) | (sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(116,plain,
% 189.44/119.24 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa))) | (~aInteger0(smndt0(xa))) | (~aInteger0(xb)) | (~aInteger0(smndt0(xb))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | (~aInteger0(smndt0(xb))) | (sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa)))))),
% 189.44/119.24 inference(monotonicity,[status(thm)],[115])).
% 189.44/119.24 tff(117,plain,
% 189.44/119.24 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa))) | (~aInteger0(smndt0(xa))) | (~aInteger0(xb)) | (~aInteger0(smndt0(xb))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | (~aInteger0(smndt0(xb))) | (sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa))))),
% 189.44/119.24 inference(transitivity,[status(thm)],[116, 114])).
% 189.44/119.24 tff(118,plain,
% 189.44/119.24 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa))) | (~aInteger0(smndt0(xa))) | (~aInteger0(xb)) | (~aInteger0(smndt0(xb))))),
% 189.44/119.24 inference(quant_inst,[status(thm)],[])).
% 189.44/119.24 tff(119,plain,
% 189.44/119.24 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(xb)) | (~aInteger0(smndt0(xa))) | (~aInteger0(smndt0(xb))) | (sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa)))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[118, 117])).
% 189.44/119.24 tff(120,plain,
% 189.44/119.24 (sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[119, 105, 23, 20, 67])).
% 189.44/119.24 tff(121,plain,
% 189.44/119.24 (sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa)) = sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))),
% 189.44/119.24 inference(symmetry,[status(thm)],[120])).
% 189.44/119.24 tff(122,plain,
% 189.44/119.24 (^[W0: $i] : refl(((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10))))))) <=> ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10))))))))),
% 189.44/119.24 inference(bind,[status(th)],[])).
% 189.44/119.24 tff(123,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10))))))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))),
% 189.44/119.24 inference(quant_intro,[status(thm)],[122])).
% 189.44/119.24 tff(124,plain,
% 189.44/119.24 (^[W0: $i] : rewrite(((~aInteger0(W0)) | ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10))))) <=> ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10))))))))),
% 189.44/119.24 inference(bind,[status(th)],[])).
% 189.44/119.24 tff(125,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10))))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))),
% 189.44/119.24 inference(quant_intro,[status(thm)],[124])).
% 189.44/119.24 tff(126,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10))))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(127,plain,
% 189.44/119.24 (^[W0: $i] : rewrite((aInteger0(W0) => ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10))))) <=> ((~aInteger0(W0)) | ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10))))))),
% 189.44/119.24 inference(bind,[status(th)],[])).
% 189.44/119.24 tff(128,plain,
% 189.44/119.24 (![W0: $i] : (aInteger0(W0) => ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10))))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))),
% 189.44/119.24 inference(quant_intro,[status(thm)],[127])).
% 189.44/119.24 tff(129,axiom,(![W0: $i] : (aInteger0(W0) => ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulMinOne')).
% 189.44/119.24 tff(130,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[129, 128])).
% 189.44/119.24 tff(131,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[130, 126])).
% 189.44/119.24 tff(132,plain,(
% 189.44/119.24 ![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(smndt0(sz10), W0) = smndt0(W0)) & (smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))),
% 189.44/119.24 inference(skolemize,[status(sab)],[131])).
% 189.44/119.24 tff(133,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[132, 125])).
% 189.44/119.24 tff(134,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[133, 123])).
% 189.44/119.24 tff(135,plain,
% 189.44/119.24 (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | ((~aInteger0(xa)) | (~((~(sdtasdt0(smndt0(sz10), xa) = smndt0(xa))) | (~(smndt0(xa) = sdtasdt0(xa, smndt0(sz10)))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | (~aInteger0(xa)) | (~((~(sdtasdt0(smndt0(sz10), xa) = smndt0(xa))) | (~(smndt0(xa) = sdtasdt0(xa, smndt0(sz10)))))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(136,plain,
% 189.44/119.24 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | ((~aInteger0(xa)) | (~((~(sdtasdt0(smndt0(sz10), xa) = smndt0(xa))) | (~(smndt0(xa) = sdtasdt0(xa, smndt0(sz10)))))))),
% 189.44/119.24 inference(quant_inst,[status(thm)],[])).
% 189.44/119.24 tff(137,plain,
% 189.44/119.24 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | (~aInteger0(xa)) | (~((~(sdtasdt0(smndt0(sz10), xa) = smndt0(xa))) | (~(smndt0(xa) = sdtasdt0(xa, smndt0(sz10))))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[136, 135])).
% 189.44/119.24 tff(138,plain,
% 189.44/119.24 (~((~(sdtasdt0(smndt0(sz10), xa) = smndt0(xa))) | (~(smndt0(xa) = sdtasdt0(xa, smndt0(sz10)))))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[137, 134, 6])).
% 189.44/119.24 tff(139,plain,
% 189.44/119.24 (((~(sdtasdt0(smndt0(sz10), xa) = smndt0(xa))) | (~(smndt0(xa) = sdtasdt0(xa, smndt0(sz10))))) | (smndt0(xa) = sdtasdt0(xa, smndt0(sz10)))),
% 189.44/119.24 inference(tautology,[status(thm)],[])).
% 189.44/119.24 tff(140,plain,
% 189.44/119.24 (smndt0(xa) = sdtasdt0(xa, smndt0(sz10))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[139, 138])).
% 189.44/119.24 tff(141,plain,
% 189.44/119.24 (^[W0: $i] : refl(((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))) <=> ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))))),
% 189.44/119.24 inference(bind,[status(th)],[])).
% 189.44/119.24 tff(142,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 189.44/119.24 inference(quant_intro,[status(thm)],[141])).
% 189.44/119.24 tff(143,plain,
% 189.44/119.24 (^[W0: $i] : rewrite(((~aInteger0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))))),
% 189.44/119.24 inference(bind,[status(th)],[])).
% 189.44/119.24 tff(144,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 189.44/119.24 inference(quant_intro,[status(thm)],[143])).
% 189.44/119.24 tff(145,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(146,plain,
% 189.44/119.24 (^[W0: $i] : rewrite((aInteger0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ((~aInteger0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))))),
% 189.44/119.24 inference(bind,[status(th)],[])).
% 189.44/119.24 tff(147,plain,
% 189.44/119.24 (![W0: $i] : (aInteger0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 189.44/119.24 inference(quant_intro,[status(thm)],[146])).
% 189.44/119.24 tff(148,axiom,(![W0: $i] : (aInteger0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulZero')).
% 189.44/119.24 tff(149,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[148, 147])).
% 189.44/119.24 tff(150,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[149, 145])).
% 189.44/119.24 tff(151,plain,(
% 189.44/119.24 ![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 189.44/119.24 inference(skolemize,[status(sab)],[150])).
% 189.44/119.24 tff(152,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[151, 144])).
% 189.44/119.24 tff(153,plain,
% 189.44/119.24 (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[152, 142])).
% 189.44/119.24 tff(154,plain,
% 189.44/119.24 (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aInteger0(xa)) | (~((~(sdtasdt0(xa, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xa))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aInteger0(xa)) | (~((~(sdtasdt0(xa, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xa))))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(155,plain,
% 189.44/119.24 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aInteger0(xa)) | (~((~(sdtasdt0(xa, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xa))))))),
% 189.44/119.24 inference(quant_inst,[status(thm)],[])).
% 189.44/119.24 tff(156,plain,
% 189.44/119.24 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aInteger0(xa)) | (~((~(sdtasdt0(xa, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xa)))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[155, 154])).
% 189.44/119.24 tff(157,plain,
% 189.44/119.24 (~((~(sdtasdt0(xa, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xa))))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[156, 153, 6])).
% 189.44/119.24 tff(158,plain,
% 189.44/119.24 (((~(sdtasdt0(xa, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xa)))) | (sdtasdt0(xa, sz00) = sz00)),
% 189.44/119.24 inference(tautology,[status(thm)],[])).
% 189.44/119.24 tff(159,plain,
% 189.44/119.24 (sdtasdt0(xa, sz00) = sz00),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[158, 157])).
% 189.44/119.24 tff(160,plain,
% 189.44/119.24 (sz00 = sdtasdt0(xa, sz00)),
% 189.44/119.24 inference(symmetry,[status(thm)],[159])).
% 189.44/119.24 tff(161,plain,
% 189.44/119.24 (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aInteger0(xb)) | (~((~(sdtpldt0(xb, smndt0(xb)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xb), xb))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aInteger0(xb)) | (~((~(sdtpldt0(xb, smndt0(xb)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xb), xb))))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(162,plain,
% 189.44/119.24 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aInteger0(xb)) | (~((~(sdtpldt0(xb, smndt0(xb)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xb), xb))))))),
% 189.44/119.24 inference(quant_inst,[status(thm)],[])).
% 189.44/119.24 tff(163,plain,
% 189.44/119.24 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aInteger0(xb)) | (~((~(sdtpldt0(xb, smndt0(xb)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xb), xb)))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[162, 161])).
% 189.44/119.24 tff(164,plain,
% 189.44/119.24 (~((~(sdtpldt0(xb, smndt0(xb)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xb), xb))))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[163, 80, 23])).
% 189.44/119.24 tff(165,plain,
% 189.44/119.24 (((~(sdtpldt0(xb, smndt0(xb)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xb), xb)))) | (sz00 = sdtpldt0(smndt0(xb), xb))),
% 189.44/119.24 inference(tautology,[status(thm)],[])).
% 189.44/119.24 tff(166,plain,
% 189.44/119.24 (sz00 = sdtpldt0(smndt0(xb), xb)),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[165, 164])).
% 189.44/119.24 tff(167,plain,
% 189.44/119.24 (sdtpldt0(smndt0(xb), xb) = sz00),
% 189.44/119.24 inference(symmetry,[status(thm)],[166])).
% 189.44/119.24 tff(168,plain,
% 189.44/119.24 (sdtpldt0(smndt0(xb), xb) = sdtasdt0(xa, sz00)),
% 189.44/119.24 inference(transitivity,[status(thm)],[167, 160])).
% 189.44/119.24 tff(169,plain,
% 189.44/119.24 (sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa)) = sdtpldt0(sdtasdt0(xa, sz00), sdtasdt0(xa, smndt0(sz10)))),
% 189.44/119.24 inference(monotonicity,[status(thm)],[168, 140])).
% 189.44/119.24 tff(170,plain,
% 189.44/119.24 (sdtpldt0(sdtasdt0(xa, sz00), sdtasdt0(xa, smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xb), xb), smndt0(xa))),
% 189.44/119.24 inference(symmetry,[status(thm)],[169])).
% 189.44/119.24 tff(171,plain,
% 189.44/119.24 (sdtasdt0(xa, smndt0(sz10)) = smndt0(xa)),
% 189.44/119.24 inference(symmetry,[status(thm)],[140])).
% 189.44/119.24 tff(172,plain,
% 189.44/119.24 (sdtpldt0(sdtasdt0(xa, sz00), sdtasdt0(xa, smndt0(sz10))) = sdtpldt0(sz00, smndt0(xa))),
% 189.44/119.24 inference(monotonicity,[status(thm)],[159, 171])).
% 189.44/119.24 tff(173,plain,
% 189.44/119.24 (sdtpldt0(sz00, smndt0(xa)) = sdtpldt0(sdtasdt0(xa, sz00), sdtasdt0(xa, smndt0(sz10)))),
% 189.44/119.24 inference(symmetry,[status(thm)],[172])).
% 189.44/119.24 tff(174,plain,
% 189.44/119.24 (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(smndt0(xa))) | (~((~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))) | (~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(smndt0(xa))) | (~((~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))) | (~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa))))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(175,plain,
% 189.44/119.24 (((~aInteger0(smndt0(xa))) | (~((~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa))) | (~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa))))))) <=> ((~aInteger0(smndt0(xa))) | (~((~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))) | (~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa))))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(176,plain,
% 189.44/119.24 (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(smndt0(xa))) | (~((~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa))) | (~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(smndt0(xa))) | (~((~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))) | (~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa)))))))),
% 189.44/119.24 inference(monotonicity,[status(thm)],[175])).
% 189.44/119.24 tff(177,plain,
% 189.44/119.24 (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(smndt0(xa))) | (~((~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa))) | (~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(smndt0(xa))) | (~((~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))) | (~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa))))))),
% 189.44/119.24 inference(transitivity,[status(thm)],[176, 174])).
% 189.44/119.24 tff(178,plain,
% 189.44/119.24 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(smndt0(xa))) | (~((~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa))) | (~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))))))),
% 189.44/119.24 inference(quant_inst,[status(thm)],[])).
% 189.44/119.24 tff(179,plain,
% 189.44/119.24 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(smndt0(xa))) | (~((~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))) | (~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa)))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[178, 177])).
% 189.44/119.24 tff(180,plain,
% 189.44/119.24 (~((~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))) | (~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa))))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[179, 56, 20])).
% 189.44/119.24 tff(181,plain,
% 189.44/119.24 (((~(smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))) | (~(sdtpldt0(smndt0(xa), sz00) = smndt0(xa)))) | (smndt0(xa) = sdtpldt0(sz00, smndt0(xa)))),
% 189.44/119.24 inference(tautology,[status(thm)],[])).
% 189.44/119.24 tff(182,plain,
% 189.44/119.24 (smndt0(xa) = sdtpldt0(sz00, smndt0(xa))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[181, 180])).
% 189.44/119.24 tff(183,plain,
% 189.44/119.24 (sdtasdt0(xa, smndt0(sz10)) = sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa)))),
% 189.44/119.24 inference(transitivity,[status(thm)],[171, 182, 173, 170, 121])).
% 189.44/119.24 tff(184,plain,
% 189.44/119.24 (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | ((~aInteger0(smndt0(xb))) | (~((~(sdtasdt0(smndt0(sz10), smndt0(xb)) = smndt0(smndt0(xb)))) | (~(smndt0(smndt0(xb)) = sdtasdt0(smndt0(xb), smndt0(sz10)))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | (~aInteger0(smndt0(xb))) | (~((~(sdtasdt0(smndt0(sz10), smndt0(xb)) = smndt0(smndt0(xb)))) | (~(smndt0(smndt0(xb)) = sdtasdt0(smndt0(xb), smndt0(sz10)))))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(185,plain,
% 189.44/119.24 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | ((~aInteger0(smndt0(xb))) | (~((~(sdtasdt0(smndt0(sz10), smndt0(xb)) = smndt0(smndt0(xb)))) | (~(smndt0(smndt0(xb)) = sdtasdt0(smndt0(xb), smndt0(sz10)))))))),
% 189.44/119.24 inference(quant_inst,[status(thm)],[])).
% 189.44/119.24 tff(186,plain,
% 189.44/119.24 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | (~aInteger0(smndt0(xb))) | (~((~(sdtasdt0(smndt0(sz10), smndt0(xb)) = smndt0(smndt0(xb)))) | (~(smndt0(smndt0(xb)) = sdtasdt0(smndt0(xb), smndt0(sz10))))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[185, 184])).
% 189.44/119.24 tff(187,plain,
% 189.44/119.24 (~((~(sdtasdt0(smndt0(sz10), smndt0(xb)) = smndt0(smndt0(xb)))) | (~(smndt0(smndt0(xb)) = sdtasdt0(smndt0(xb), smndt0(sz10)))))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[186, 134, 67])).
% 189.44/119.24 tff(188,plain,
% 189.44/119.24 (((~(sdtasdt0(smndt0(sz10), smndt0(xb)) = smndt0(smndt0(xb)))) | (~(smndt0(smndt0(xb)) = sdtasdt0(smndt0(xb), smndt0(sz10))))) | (smndt0(smndt0(xb)) = sdtasdt0(smndt0(xb), smndt0(sz10)))),
% 189.44/119.24 inference(tautology,[status(thm)],[])).
% 189.44/119.24 tff(189,plain,
% 189.44/119.24 (smndt0(smndt0(xb)) = sdtasdt0(smndt0(xb), smndt0(sz10))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[188, 187])).
% 189.44/119.24 tff(190,plain,
% 189.44/119.24 (sdtasdt0(smndt0(xb), smndt0(sz10)) = smndt0(smndt0(xb))),
% 189.44/119.24 inference(symmetry,[status(thm)],[189])).
% 189.44/119.24 tff(191,plain,
% 189.44/119.24 (sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10))) = sdtpldt0(smndt0(smndt0(xb)), sdtpldt0(smndt0(xb), sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.24 inference(monotonicity,[status(thm)],[190, 183])).
% 189.44/119.24 tff(192,plain,
% 189.44/119.24 (aInteger0(sz10) <=> aInteger0(sz10)),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(193,axiom,(aInteger0(sz10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mIntOne')).
% 189.44/119.24 tff(194,plain,
% 189.44/119.24 (aInteger0(sz10)),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[193, 192])).
% 189.44/119.24 tff(195,plain,
% 189.44/119.24 (((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(sz10)) | (~aInteger0(sz10)))) <=> ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(sz10)) | (~aInteger0(sz10)))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(196,plain,
% 189.44/119.24 ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(sz10)) | (~aInteger0(sz10)))),
% 189.44/119.24 inference(quant_inst,[status(thm)],[])).
% 189.44/119.24 tff(197,plain,
% 189.44/119.24 ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(sz10)) | (~aInteger0(sz10))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[196, 195])).
% 189.44/119.24 tff(198,plain,
% 189.44/119.24 (aInteger0(smndt0(sz10))),
% 189.44/119.24 inference(unit_resolution,[status(thm)],[197, 194, 16])).
% 189.44/119.24 tff(199,plain,
% 189.44/119.24 (^[W0: $i, W1: $i, W2: $i] : refl(((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))))),
% 189.44/119.24 inference(bind,[status(th)],[])).
% 189.44/119.24 tff(200,plain,
% 189.44/119.24 (![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))),
% 189.44/119.24 inference(quant_intro,[status(thm)],[199])).
% 189.44/119.24 tff(201,plain,
% 189.44/119.24 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) <=> (~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))), ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) <=> (~(~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))))), rewrite((~(~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))), ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))), rewrite(((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))) <=> (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))), (((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> (((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))))), rewrite((((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))), (((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))))),
% 189.44/119.24 inference(bind,[status(th)],[])).
% 189.44/119.24 tff(202,plain,
% 189.44/119.24 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))),
% 189.44/119.24 inference(quant_intro,[status(thm)],[201])).
% 189.44/119.24 tff(203,plain,
% 189.44/119.24 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(204,plain,
% 189.44/119.24 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) <=> (aInteger0(W0) & aInteger0(W1) & aInteger0(W2))), ((((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))), rewrite(((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))), ((((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))),
% 189.44/119.24 inference(bind,[status(th)],[])).
% 189.44/119.24 tff(205,plain,
% 189.44/119.24 (![W0: $i, W1: $i, W2: $i] : (((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))),
% 189.44/119.24 inference(quant_intro,[status(thm)],[204])).
% 189.44/119.24 tff(206,axiom,(![W0: $i, W1: $i, W2: $i] : (((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDistrib')).
% 189.44/119.24 tff(207,plain,
% 189.44/119.24 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[206, 205])).
% 189.44/119.24 tff(208,plain,
% 189.44/119.24 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[207, 203])).
% 189.44/119.24 tff(209,plain,(
% 189.44/119.24 ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))),
% 189.44/119.24 inference(skolemize,[status(sab)],[208])).
% 189.44/119.24 tff(210,plain,
% 189.44/119.24 (![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[209, 202])).
% 189.44/119.24 tff(211,plain,
% 189.44/119.24 (![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))),
% 189.44/119.24 inference(modus_ponens,[status(thm)],[210, 200])).
% 189.44/119.24 tff(212,plain,
% 189.44/119.24 (((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | ((~aInteger0(xa)) | (~aInteger0(smndt0(xb))) | (~aInteger0(smndt0(sz10))) | (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb))) | (~aInteger0(smndt0(sz10))) | (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10))))))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(213,plain,
% 189.44/119.24 (((~aInteger0(smndt0(sz10))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb))) | (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10)))))))) <=> ((~aInteger0(xa)) | (~aInteger0(smndt0(xb))) | (~aInteger0(smndt0(sz10))) | (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10))))))))),
% 189.44/119.24 inference(rewrite,[status(thm)],[])).
% 189.44/119.24 tff(214,plain,
% 189.44/119.24 (((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | ((~aInteger0(smndt0(sz10))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb))) | (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | ((~aInteger0(xa)) | (~aInteger0(smndt0(xb))) | (~aInteger0(smndt0(sz10))) | (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10)))))))))),
% 189.44/119.25 inference(monotonicity,[status(thm)],[213])).
% 189.44/119.25 tff(215,plain,
% 189.44/119.25 (((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | ((~aInteger0(smndt0(sz10))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb))) | (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb))) | (~aInteger0(smndt0(sz10))) | (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10))))))))),
% 189.44/119.25 inference(transitivity,[status(thm)],[214, 212])).
% 189.44/119.25 tff(216,plain,
% 189.44/119.25 ((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | ((~aInteger0(smndt0(sz10))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb))) | (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10))))))))),
% 189.44/119.25 inference(quant_inst,[status(thm)],[])).
% 189.44/119.25 tff(217,plain,
% 189.44/119.25 ((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb))) | (~aInteger0(smndt0(sz10))) | (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10)))))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[216, 215])).
% 189.44/119.25 tff(218,plain,
% 189.44/119.25 (~((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10))))))),
% 189.44/119.25 inference(unit_resolution,[status(thm)],[217, 211, 6, 67, 198])).
% 189.44/119.25 tff(219,plain,
% 189.44/119.25 (((~(sdtasdt0(smndt0(xb), sdtpldt0(xa, smndt0(sz10))) = sdtpldt0(sdtasdt0(smndt0(xb), xa), sdtasdt0(smndt0(xb), smndt0(sz10))))) | (~(sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10)))))) | (sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10))))),
% 189.44/119.25 inference(tautology,[status(thm)],[])).
% 189.44/119.25 tff(220,plain,
% 189.44/119.25 (sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb), smndt0(sz10)), sdtasdt0(xa, smndt0(sz10)))),
% 189.44/119.25 inference(unit_resolution,[status(thm)],[219, 218])).
% 189.44/119.25 tff(221,plain,
% 189.44/119.25 (^[W0: $i, W1: $i] : refl(((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0))))),
% 189.44/119.25 inference(bind,[status(th)],[])).
% 189.44/119.25 tff(222,plain,
% 189.44/119.25 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.25 inference(quant_intro,[status(thm)],[221])).
% 189.44/119.25 tff(223,plain,
% 189.44/119.25 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & aInteger0(W1)) <=> (~((~aInteger0(W1)) | (~aInteger0(W0))))), ((~(aInteger0(W0) & aInteger0(W1))) <=> (~(~((~aInteger0(W1)) | (~aInteger0(W0))))))), rewrite((~(~((~aInteger0(W1)) | (~aInteger0(W0))))) <=> ((~aInteger0(W1)) | (~aInteger0(W0)))), ((~(aInteger0(W0) & aInteger0(W1))) <=> ((~aInteger0(W1)) | (~aInteger0(W0))))), (((~(aInteger0(W0) & aInteger0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> (((~aInteger0(W1)) | (~aInteger0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))), rewrite((((~aInteger0(W1)) | (~aInteger0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))), (((~(aInteger0(W0) & aInteger0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))))),
% 189.44/119.25 inference(bind,[status(th)],[])).
% 189.44/119.25 tff(224,plain,
% 189.44/119.25 (![W0: $i, W1: $i] : ((~(aInteger0(W0) & aInteger0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.25 inference(quant_intro,[status(thm)],[223])).
% 189.44/119.25 tff(225,plain,
% 189.44/119.25 (![W0: $i, W1: $i] : ((~(aInteger0(W0) & aInteger0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aInteger0(W0) & aInteger0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(226,plain,
% 189.44/119.25 (^[W0: $i, W1: $i] : rewrite(((aInteger0(W0) & aInteger0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((~(aInteger0(W0) & aInteger0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))),
% 189.44/119.25 inference(bind,[status(th)],[])).
% 189.44/119.25 tff(227,plain,
% 189.44/119.25 (![W0: $i, W1: $i] : ((aInteger0(W0) & aInteger0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aInteger0(W0) & aInteger0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 189.44/119.25 inference(quant_intro,[status(thm)],[226])).
% 189.44/119.25 tff(228,axiom,(![W0: $i, W1: $i] : ((aInteger0(W0) & aInteger0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddComm')).
% 189.44/119.25 tff(229,plain,
% 189.44/119.25 (![W0: $i, W1: $i] : ((~(aInteger0(W0) & aInteger0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[228, 227])).
% 189.44/119.25 tff(230,plain,
% 189.44/119.25 (![W0: $i, W1: $i] : ((~(aInteger0(W0) & aInteger0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[229, 225])).
% 189.44/119.25 tff(231,plain,(
% 189.44/119.25 ![W0: $i, W1: $i] : ((~(aInteger0(W0) & aInteger0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 189.44/119.25 inference(skolemize,[status(sab)],[230])).
% 189.44/119.25 tff(232,plain,
% 189.44/119.25 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[231, 224])).
% 189.44/119.25 tff(233,plain,
% 189.44/119.25 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[232, 222])).
% 189.44/119.25 tff(234,plain,
% 189.44/119.25 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(xa)) | (sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))) | (~aInteger0(smndt0(xb))))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(xa)) | (sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))) | (~aInteger0(smndt0(xb))))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(235,plain,
% 189.44/119.25 (((sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb)))) <=> ((~aInteger0(xa)) | (sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))) | (~aInteger0(smndt0(xb))))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(236,plain,
% 189.44/119.25 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb))))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(xa)) | (sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))) | (~aInteger0(smndt0(xb)))))),
% 189.44/119.25 inference(monotonicity,[status(thm)],[235])).
% 189.44/119.25 tff(237,plain,
% 189.44/119.25 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb))))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(xa)) | (sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))) | (~aInteger0(smndt0(xb))))),
% 189.44/119.25 inference(transitivity,[status(thm)],[236, 234])).
% 189.44/119.25 tff(238,plain,
% 189.44/119.25 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))) | (~aInteger0(xa)) | (~aInteger0(smndt0(xb))))),
% 189.44/119.25 inference(quant_inst,[status(thm)],[])).
% 189.44/119.25 tff(239,plain,
% 189.44/119.25 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(xa)) | (sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))) | (~aInteger0(smndt0(xb)))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[238, 237])).
% 189.44/119.25 tff(240,plain,
% 189.44/119.25 (sdtpldt0(smndt0(xb), xa) = sdtpldt0(xa, smndt0(xb))),
% 189.44/119.25 inference(unit_resolution,[status(thm)],[239, 233, 6, 67])).
% 189.44/119.25 tff(241,plain,
% 189.44/119.25 (sdtpldt0(xa, smndt0(xb)) = sdtpldt0(smndt0(xb), xa)),
% 189.44/119.25 inference(symmetry,[status(thm)],[240])).
% 189.44/119.25 tff(242,plain,
% 189.44/119.25 (sdtasdt0(sdtpldt0(xa, smndt0(xb)), smndt0(sz10)) = sdtasdt0(sdtpldt0(smndt0(xb), xa), smndt0(sz10))),
% 189.44/119.25 inference(monotonicity,[status(thm)],[241])).
% 189.44/119.25 tff(243,plain,
% 189.44/119.25 (?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xa, smndt0(xb)))) <=> ?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xa, smndt0(xb))))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(244,plain,
% 189.44/119.25 ((~(((?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xa, smndt0(xb)))) & aDivisorOf0(xq, sdtpldt0(xa, smndt0(xb)))) & sdteqdtlpzmzozddtrp0(xa, xb, xq)) => ((?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))) | aDivisorOf0(xq, sdtpldt0(xb, smndt0(xa)))) | sdteqdtlpzmzozddtrp0(xb, xa, xq)))) <=> (~(aDivisorOf0(xq, sdtpldt0(xb, smndt0(xa))) | sdteqdtlpzmzozddtrp0(xb, xa, xq) | ?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))) | (~(?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xa, smndt0(xb)))) & aDivisorOf0(xq, sdtpldt0(xa, smndt0(xb))) & sdteqdtlpzmzozddtrp0(xa, xb, xq)))))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(245,axiom,(~(((?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xa, smndt0(xb)))) & aDivisorOf0(xq, sdtpldt0(xa, smndt0(xb)))) & sdteqdtlpzmzozddtrp0(xa, xb, xq)) => ((?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))) | aDivisorOf0(xq, sdtpldt0(xb, smndt0(xa)))) | sdteqdtlpzmzozddtrp0(xb, xa, xq)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 189.44/119.25 tff(246,plain,
% 189.44/119.25 (~(aDivisorOf0(xq, sdtpldt0(xb, smndt0(xa))) | sdteqdtlpzmzozddtrp0(xb, xa, xq) | ?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))) | (~(?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xa, smndt0(xb)))) & aDivisorOf0(xq, sdtpldt0(xa, smndt0(xb))) & sdteqdtlpzmzozddtrp0(xa, xb, xq))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[245, 244])).
% 189.44/119.25 tff(247,plain,
% 189.44/119.25 (?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xa, smndt0(xb)))) & aDivisorOf0(xq, sdtpldt0(xa, smndt0(xb))) & sdteqdtlpzmzozddtrp0(xa, xb, xq)),
% 189.44/119.25 inference(or_elim,[status(thm)],[246])).
% 189.44/119.25 tff(248,plain,
% 189.44/119.25 (?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xa, smndt0(xb))))),
% 189.44/119.25 inference(and_elim,[status(thm)],[247])).
% 189.44/119.25 tff(249,plain,
% 189.44/119.25 (?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xa, smndt0(xb))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[248, 243])).
% 189.44/119.25 tff(250,plain,(
% 189.44/119.25 aInteger0(W0!1) & (sdtasdt0(xq, W0!1) = sdtpldt0(xa, smndt0(xb)))),
% 189.44/119.25 inference(skolemize,[status(sab)],[249])).
% 189.44/119.25 tff(251,plain,
% 189.44/119.25 (sdtasdt0(xq, W0!1) = sdtpldt0(xa, smndt0(xb))),
% 189.44/119.25 inference(and_elim,[status(thm)],[250])).
% 189.44/119.25 tff(252,plain,
% 189.44/119.25 (sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10)) = sdtasdt0(sdtpldt0(xa, smndt0(xb)), smndt0(sz10))),
% 189.44/119.25 inference(monotonicity,[status(thm)],[251])).
% 189.44/119.25 tff(253,plain,
% 189.44/119.25 (aInteger0(W0!1)),
% 189.44/119.25 inference(and_elim,[status(thm)],[250])).
% 189.44/119.25 tff(254,plain,
% 189.44/119.25 (aInteger0(xq) <=> aInteger0(xq)),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(255,plain,
% 189.44/119.25 (aInteger0(xq)),
% 189.44/119.25 inference(and_elim,[status(thm)],[3])).
% 189.44/119.25 tff(256,plain,
% 189.44/119.25 (aInteger0(xq)),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[255, 254])).
% 189.44/119.25 tff(257,plain,
% 189.44/119.25 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))),
% 189.44/119.25 inference(bind,[status(th)],[])).
% 189.44/119.25 tff(258,plain,
% 189.44/119.25 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.25 inference(quant_intro,[status(thm)],[257])).
% 189.44/119.25 tff(259,plain,
% 189.44/119.25 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) <=> (~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))), ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) <=> (~(~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))))), rewrite((~(~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))), ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))), (((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))) <=> (((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))))), rewrite((((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))) <=> ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))), (((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))) <=> ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))))),
% 189.44/119.25 inference(bind,[status(th)],[])).
% 189.44/119.25 tff(260,plain,
% 189.44/119.25 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.25 inference(quant_intro,[status(thm)],[259])).
% 189.44/119.25 tff(261,plain,
% 189.44/119.25 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(262,plain,
% 189.44/119.25 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) <=> (aInteger0(W0) & aInteger0(W1) & aInteger0(W2))), ((((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))) <=> ((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) => (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))))), rewrite(((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) => (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))) <=> ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)))), ((((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))) <=> ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)))))),
% 189.44/119.25 inference(bind,[status(th)],[])).
% 189.44/119.25 tff(263,plain,
% 189.44/119.25 (![W0: $i, W1: $i, W2: $i] : (((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)))),
% 189.44/119.25 inference(quant_intro,[status(thm)],[262])).
% 189.44/119.25 tff(264,axiom,(![W0: $i, W1: $i, W2: $i] : (((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulAsso')).
% 189.44/119.25 tff(265,plain,
% 189.44/119.25 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[264, 263])).
% 189.44/119.25 tff(266,plain,
% 189.44/119.25 (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[265, 261])).
% 189.44/119.25 tff(267,plain,(
% 189.44/119.25 ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)))),
% 189.44/119.25 inference(skolemize,[status(sab)],[266])).
% 189.44/119.25 tff(268,plain,
% 189.44/119.25 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[267, 260])).
% 189.44/119.25 tff(269,plain,
% 189.44/119.25 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[268, 258])).
% 189.44/119.25 tff(270,plain,
% 189.44/119.25 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(W0!1)) | (~aInteger0(xq)) | (~aInteger0(smndt0(sz10))) | (sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(W0!1)) | (~aInteger0(xq)) | (~aInteger0(smndt0(sz10))) | (sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10))))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(271,plain,
% 189.44/119.25 (((sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(W0!1)) | (~aInteger0(xq))) <=> ((~aInteger0(W0!1)) | (~aInteger0(xq)) | (~aInteger0(smndt0(sz10))) | (sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10))))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(272,plain,
% 189.44/119.25 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(W0!1)) | (~aInteger0(xq)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(W0!1)) | (~aInteger0(xq)) | (~aInteger0(smndt0(sz10))) | (sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10)))))),
% 189.44/119.25 inference(monotonicity,[status(thm)],[271])).
% 189.44/119.25 tff(273,plain,
% 189.44/119.25 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(W0!1)) | (~aInteger0(xq)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(W0!1)) | (~aInteger0(xq)) | (~aInteger0(smndt0(sz10))) | (sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10))))),
% 189.44/119.25 inference(transitivity,[status(thm)],[272, 270])).
% 189.44/119.25 tff(274,plain,
% 189.44/119.25 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(W0!1)) | (~aInteger0(xq)))),
% 189.44/119.25 inference(quant_inst,[status(thm)],[])).
% 189.44/119.25 tff(275,plain,
% 189.44/119.25 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(W0, sdtasdt0(W1, W2)) = sdtasdt0(sdtasdt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(W0!1)) | (~aInteger0(xq)) | (~aInteger0(smndt0(sz10))) | (sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10)))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[274, 273])).
% 189.44/119.25 tff(276,plain,
% 189.44/119.25 (sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10))) = sdtasdt0(sdtasdt0(xq, W0!1), smndt0(sz10))),
% 189.44/119.25 inference(unit_resolution,[status(thm)],[275, 269, 256, 253, 198])).
% 189.44/119.25 tff(277,plain,
% 189.44/119.25 (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | ((~aInteger0(W0!1)) | (~((~(sdtasdt0(smndt0(sz10), W0!1) = smndt0(W0!1))) | (~(smndt0(W0!1) = sdtasdt0(W0!1, smndt0(sz10)))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | (~aInteger0(W0!1)) | (~((~(sdtasdt0(smndt0(sz10), W0!1) = smndt0(W0!1))) | (~(smndt0(W0!1) = sdtasdt0(W0!1, smndt0(sz10)))))))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(278,plain,
% 189.44/119.25 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | ((~aInteger0(W0!1)) | (~((~(sdtasdt0(smndt0(sz10), W0!1) = smndt0(W0!1))) | (~(smndt0(W0!1) = sdtasdt0(W0!1, smndt0(sz10)))))))),
% 189.44/119.25 inference(quant_inst,[status(thm)],[])).
% 189.44/119.25 tff(279,plain,
% 189.44/119.25 ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(smndt0(sz10), W0) = smndt0(W0))) | (~(smndt0(W0) = sdtasdt0(W0, smndt0(sz10)))))))) | (~aInteger0(W0!1)) | (~((~(sdtasdt0(smndt0(sz10), W0!1) = smndt0(W0!1))) | (~(smndt0(W0!1) = sdtasdt0(W0!1, smndt0(sz10))))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[278, 277])).
% 189.44/119.25 tff(280,plain,
% 189.44/119.25 (~((~(sdtasdt0(smndt0(sz10), W0!1) = smndt0(W0!1))) | (~(smndt0(W0!1) = sdtasdt0(W0!1, smndt0(sz10)))))),
% 189.44/119.25 inference(unit_resolution,[status(thm)],[279, 134, 253])).
% 189.44/119.25 tff(281,plain,
% 189.44/119.25 (((~(sdtasdt0(smndt0(sz10), W0!1) = smndt0(W0!1))) | (~(smndt0(W0!1) = sdtasdt0(W0!1, smndt0(sz10))))) | (smndt0(W0!1) = sdtasdt0(W0!1, smndt0(sz10)))),
% 189.44/119.25 inference(tautology,[status(thm)],[])).
% 189.44/119.25 tff(282,plain,
% 189.44/119.25 (smndt0(W0!1) = sdtasdt0(W0!1, smndt0(sz10))),
% 189.44/119.25 inference(unit_resolution,[status(thm)],[281, 280])).
% 189.44/119.25 tff(283,plain,
% 189.44/119.25 (sdtasdt0(xq, smndt0(W0!1)) = sdtasdt0(xq, sdtasdt0(W0!1, smndt0(sz10)))),
% 189.44/119.25 inference(monotonicity,[status(thm)],[282])).
% 189.44/119.25 tff(284,plain,
% 189.44/119.25 (sdtasdt0(xq, smndt0(W0!1)) = sdtpldt0(xb, smndt0(xa))),
% 189.44/119.25 inference(transitivity,[status(thm)],[283, 276, 252, 242, 220, 191, 113, 88, 63])).
% 189.44/119.25 tff(285,plain,
% 189.44/119.25 (((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(W0!1)) | (~aInteger0(W0!1)))) <=> ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(W0!1)) | (~aInteger0(W0!1)))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(286,plain,
% 189.44/119.25 ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(W0!1)) | (~aInteger0(W0!1)))),
% 189.44/119.25 inference(quant_inst,[status(thm)],[])).
% 189.44/119.25 tff(287,plain,
% 189.44/119.25 ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(W0!1)) | (~aInteger0(W0!1))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[286, 285])).
% 189.44/119.25 tff(288,plain,
% 189.44/119.25 (aInteger0(smndt0(W0!1))),
% 189.44/119.25 inference(unit_resolution,[status(thm)],[287, 16, 253])).
% 189.44/119.25 tff(289,plain,
% 189.44/119.25 (^[W0: $i] : refl(((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))) <=> ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))))),
% 189.44/119.25 inference(bind,[status(th)],[])).
% 189.44/119.25 tff(290,plain,
% 189.44/119.25 (![W0: $i] : ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.25 inference(quant_intro,[status(thm)],[289])).
% 189.44/119.25 tff(291,plain,
% 189.44/119.25 (^[W0: $i] : trans(monotonicity(rewrite((aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))) <=> (~((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))))), ((~(aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))) <=> (~(~((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))))))), rewrite((~(~((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))))) <=> ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))), ((~(aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))) <=> ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))))),
% 189.44/119.25 inference(bind,[status(th)],[])).
% 189.44/119.25 tff(292,plain,
% 189.44/119.25 (![W0: $i] : (~(aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.25 inference(quant_intro,[status(thm)],[291])).
% 189.44/119.25 tff(293,plain,
% 189.44/119.25 ((~?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))) <=> (~?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.25 inference(rewrite,[status(thm)],[])).
% 189.44/119.25 tff(294,plain,
% 189.44/119.25 (~?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.25 inference(or_elim,[status(thm)],[246])).
% 189.44/119.25 tff(295,plain,
% 189.44/119.25 (~?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[294, 293])).
% 189.44/119.25 tff(296,plain,
% 189.44/119.25 (~?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[295, 293])).
% 189.44/119.25 tff(297,plain,
% 189.44/119.25 (~?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[296, 293])).
% 189.44/119.25 tff(298,plain,
% 189.44/119.25 (~?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[297, 293])).
% 189.44/119.25 tff(299,plain,
% 189.44/119.25 (~?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[298, 293])).
% 189.44/119.25 tff(300,plain,
% 189.44/119.25 (~?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[299, 293])).
% 189.44/119.25 tff(301,plain,
% 189.44/119.25 (^[W0: $i] : refl($oeq((~(aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa))))), (~(aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))))),
% 189.44/119.25 inference(bind,[status(th)],[])).
% 189.44/119.25 tff(302,plain,(
% 189.44/119.25 ![W0: $i] : (~(aInteger0(W0) & (sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.25 inference(nnf-neg,[status(sab)],[300, 301])).
% 189.44/119.25 tff(303,plain,
% 189.44/119.25 (![W0: $i] : ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[302, 292])).
% 189.44/119.25 tff(304,plain,
% 189.44/119.25 (![W0: $i] : ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.25 inference(modus_ponens,[status(thm)],[303, 290])).
% 189.44/119.25 tff(305,plain,
% 189.44/119.25 (((~![W0: $i] : ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))) | ((~aInteger0(smndt0(W0!1))) | (~(sdtasdt0(xq, smndt0(W0!1)) = sdtpldt0(xb, smndt0(xa)))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))) | (~aInteger0(smndt0(W0!1))) | (~(sdtasdt0(xq, smndt0(W0!1)) = sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.26 inference(rewrite,[status(thm)],[])).
% 189.44/119.26 tff(306,plain,
% 189.44/119.26 ((~![W0: $i] : ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))) | ((~aInteger0(smndt0(W0!1))) | (~(sdtasdt0(xq, smndt0(W0!1)) = sdtpldt0(xb, smndt0(xa)))))),
% 189.44/119.26 inference(quant_inst,[status(thm)],[])).
% 189.44/119.26 tff(307,plain,
% 189.44/119.26 ((~![W0: $i] : ((~aInteger0(W0)) | (~(sdtasdt0(xq, W0) = sdtpldt0(xb, smndt0(xa)))))) | (~aInteger0(smndt0(W0!1))) | (~(sdtasdt0(xq, smndt0(W0!1)) = sdtpldt0(xb, smndt0(xa))))),
% 189.44/119.26 inference(modus_ponens,[status(thm)],[306, 305])).
% 189.44/119.26 tff(308,plain,
% 189.44/119.26 (~(sdtasdt0(xq, smndt0(W0!1)) = sdtpldt0(xb, smndt0(xa)))),
% 189.44/119.26 inference(unit_resolution,[status(thm)],[307, 304, 288])).
% 189.44/119.26 tff(309,plain,
% 189.44/119.26 ($false),
% 189.44/119.26 inference(unit_resolution,[status(thm)],[308, 284])).
% 189.44/119.26 % SZS output end Proof
%------------------------------------------------------------------------------