TSTP Solution File: RNG112+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG112+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 : Tue Sep 20 03:18:28 EDT 2022
% Result : Theorem 0.53s 0.57s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG112+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 22:36:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.53/0.57 % SZS status Theorem
% 0.53/0.57 % SZS output start Proof
% 0.53/0.57 tff(aElementOf0_type, type, (
% 0.53/0.57 aElementOf0: ( $i * $i ) > $o)).
% 0.53/0.57 tff(sdtpldt1_type, type, (
% 0.53/0.57 sdtpldt1: ( $i * $i ) > $i)).
% 0.53/0.57 tff(slsdtgt0_type, type, (
% 0.53/0.57 slsdtgt0: $i > $i)).
% 0.53/0.57 tff(xb_type, type, (
% 0.53/0.57 xb: $i)).
% 0.53/0.57 tff(xa_type, type, (
% 0.53/0.57 xa: $i)).
% 0.53/0.57 tff(tptp_fun_W1_22_type, type, (
% 0.53/0.57 tptp_fun_W1_22: $i > $i)).
% 0.53/0.57 tff(tptp_fun_W1_21_type, type, (
% 0.53/0.57 tptp_fun_W1_21: $i)).
% 0.53/0.57 tff(sz00_type, type, (
% 0.53/0.57 sz00: $i)).
% 0.53/0.57 tff(iLess0_type, type, (
% 0.53/0.57 iLess0: ( $i * $i ) > $o)).
% 0.53/0.57 tff(sbrdtbr0_type, type, (
% 0.53/0.57 sbrdtbr0: $i > $i)).
% 0.53/0.57 tff(xI_type, type, (
% 0.53/0.57 xI: $i)).
% 0.53/0.57 tff(tptp_fun_W0_20_type, type, (
% 0.53/0.57 tptp_fun_W0_20: $i)).
% 0.53/0.57 tff(1,plain,
% 0.53/0.57 (^[W0: $i] : trans(monotonicity(rewrite((~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) <=> (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))), (((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))))), rewrite(((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))), (((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))))),
% 0.53/0.57 inference(bind,[status(th)],[])).
% 0.53/0.57 tff(2,plain,
% 0.53/0.57 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))),
% 0.53/0.57 inference(quant_intro,[status(thm)],[1])).
% 0.53/0.57 tff(3,plain,
% 0.53/0.57 (^[W0: $i] : refl(((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))),
% 0.53/0.57 inference(bind,[status(th)],[])).
% 0.53/0.57 tff(4,plain,
% 0.53/0.57 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.53/0.57 inference(quant_intro,[status(thm)],[3])).
% 0.53/0.57 tff(5,plain,
% 0.53/0.57 (^[W0: $i] : rewrite(((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))),
% 0.53/0.57 inference(bind,[status(th)],[])).
% 0.53/0.57 tff(6,plain,
% 0.53/0.57 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.53/0.57 inference(quant_intro,[status(thm)],[5])).
% 0.53/0.57 tff(7,plain,
% 0.53/0.57 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.53/0.57 inference(transitivity,[status(thm)],[6, 4])).
% 0.53/0.57 tff(8,plain,
% 0.53/0.57 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00))) <=> (~((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W0 = sz00)))), ((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))) <=> (~(~((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W0 = sz00)))))), rewrite((~(~((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W0 = sz00)))) <=> ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W0 = sz00))), ((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))) <=> ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W0 = sz00)))), trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00))) <=> (~((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W2 = sz00)))), ((~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00)))) <=> (~(~((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W2 = sz00)))))), rewrite((~(~((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W2 = sz00)))) <=> ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W2 = sz00))), ((~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00)))) <=> ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W2 = sz00)))), (((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00))))) <=> ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W2 = sz00))))), rewrite(((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W2 = sz00))) <=> ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))), (((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00))))) <=> ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))), (![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00))))) <=> ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))), ((aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00)))))) <=> (aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!21 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))), rewrite((aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!21 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) <=> (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))), ((aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00)))))) <=> (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))), (((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))) | (aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00))))))) <=> (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W0 = sz00)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))), rewrite((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W0 = sz00)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))), (((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))) | (aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(9,plain,
% 0.53/0.58 (![W0: $i] : ((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))) | (aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[8])).
% 0.53/0.58 tff(10,plain,
% 0.53/0.58 (^[W0: $i] : rewrite(((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))) <=> ((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00))))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(11,plain,
% 0.53/0.58 (![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))) <=> ![W0: $i] : ((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00)))))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[10])).
% 0.53/0.58 tff(12,plain,
% 0.53/0.58 (![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))) <=> ![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(13,plain,
% 0.53/0.58 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))) <=> ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))), (![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))) <=> ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))), (((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))) <=> ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))), rewrite(((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) <=> (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))), (((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))) <=> (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))))), (?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))) <=> ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))), (((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))) <=> ((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))))), rewrite(((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))) <=> ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))), (((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))) <=> ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(14,plain,
% 0.53/0.58 (![W0: $i] : ((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))) <=> ![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[13])).
% 0.53/0.58 tff(15,axiom,(![W0: $i] : ((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2351')).
% 0.53/0.58 tff(16,plain,
% 0.53/0.58 (![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.53/0.58 tff(17,plain,
% 0.53/0.58 (![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.53/0.58 tff(18,plain,
% 0.53/0.58 (![W0: $i] : ((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00)))))))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.53/0.58 tff(19,plain,(
% 0.53/0.58 ![W0: $i] : ((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))) | (aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W2 = sz00)))))))),
% 0.53/0.58 inference(skolemize,[status(sab)],[18])).
% 0.53/0.58 tff(20,plain,
% 0.53/0.58 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.53/0.58 tff(21,plain,
% 0.53/0.58 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.53/0.58 tff(22,plain,
% 0.53/0.58 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.53/0.58 tff(23,plain,
% 0.53/0.58 (?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00))) <=> ?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(24,axiom,(?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2228')).
% 0.53/0.58 tff(25,plain,
% 0.53/0.58 (?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.53/0.58 tff(26,plain,(
% 0.53/0.58 aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0!20 = sz00))),
% 0.53/0.58 inference(skolemize,[status(sab)],[25])).
% 0.53/0.58 tff(27,plain,
% 0.53/0.58 (~(W0!20 = sz00)),
% 0.53/0.58 inference(and_elim,[status(thm)],[26])).
% 0.53/0.58 tff(28,plain,
% 0.53/0.58 (aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 0.53/0.58 inference(and_elim,[status(thm)],[26])).
% 0.53/0.58 tff(29,plain,
% 0.53/0.58 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))) | ((W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))) | (W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(30,plain,
% 0.53/0.58 (((W0!20 = sz00) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))) <=> ((W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(31,plain,
% 0.53/0.58 ((~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) <=> (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(32,plain,
% 0.53/0.58 (((W0!20 = sz00) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))) <=> ((W0!20 = sz00) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))),
% 0.53/0.58 inference(monotonicity,[status(thm)],[31])).
% 0.53/0.58 tff(33,plain,
% 0.53/0.58 (((W0!20 = sz00) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))) <=> ((W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.53/0.58 inference(transitivity,[status(thm)],[32, 30])).
% 0.53/0.58 tff(34,plain,
% 0.53/0.58 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))) | ((W0!20 = sz00) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))) | ((W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))),
% 0.53/0.58 inference(monotonicity,[status(thm)],[33])).
% 0.53/0.58 tff(35,plain,
% 0.53/0.58 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))) | ((W0!20 = sz00) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))) | (W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.53/0.58 inference(transitivity,[status(thm)],[34, 29])).
% 0.53/0.58 tff(36,plain,
% 0.53/0.58 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))) | ((W0!20 = sz00) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))),
% 0.55/0.58 inference(quant_inst,[status(thm)],[])).
% 0.55/0.58 tff(37,plain,
% 0.55/0.58 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))) | (W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | (~aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))),
% 0.55/0.58 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.55/0.58 tff(38,plain,
% 0.55/0.58 (~((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.55/0.58 inference(unit_resolution,[status(thm)],[37, 28, 27, 22])).
% 0.55/0.58 tff(39,plain,
% 0.55/0.58 (((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) | aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 0.55/0.58 inference(tautology,[status(thm)],[])).
% 0.55/0.58 tff(40,plain,
% 0.55/0.58 (aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 0.55/0.58 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.55/0.58 tff(41,plain,
% 0.55/0.58 (((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) | (~(W1!21 = sz00))),
% 0.55/0.58 inference(tautology,[status(thm)],[])).
% 0.55/0.58 tff(42,plain,
% 0.55/0.58 (~(W1!21 = sz00)),
% 0.55/0.58 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.55/0.58 tff(43,plain,
% 0.55/0.58 (^[W0: $i] : refl(((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))),
% 0.55/0.58 inference(bind,[status(th)],[])).
% 0.55/0.58 tff(44,plain,
% 0.55/0.58 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.55/0.58 inference(quant_intro,[status(thm)],[43])).
% 0.55/0.58 tff(45,plain,
% 0.55/0.58 (^[W0: $i] : trans(monotonicity(rewrite((~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00)))))) <=> (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))), (((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))), rewrite(((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))), (((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(46,plain,
% 0.55/0.59 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[45])).
% 0.55/0.59 tff(47,plain,
% 0.55/0.59 (^[W0: $i] : trans(monotonicity(rewrite((~(~(W0 = sz00))) <=> (W0 = sz00)), (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~(~(W0 = sz00))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00))))))))), rewrite(((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00)))))))), (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~(~(W0 = sz00))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00)))))))))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(48,plain,
% 0.55/0.59 (![W0: $i] : ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~(~(W0 = sz00))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00)))))))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[47])).
% 0.55/0.59 tff(49,plain,
% 0.55/0.59 ((~?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))) <=> (~?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)))))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(50,plain,
% 0.55/0.59 ((~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))) <=> (~?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)))))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(51,plain,
% 0.55/0.59 ((~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))) <=> (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(52,plain,
% 0.55/0.59 ((~?[W0: $i] : ((aElementOf0(W0, xI) & (~(W0 = sz00))) & ![W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) => (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0)))))) <=> (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(53,axiom,(~?[W0: $i] : ((aElementOf0(W0, xI) & (~(W0 = sz00))) & ![W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) => (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.55/0.59 tff(54,plain,
% 0.55/0.59 (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.55/0.59 tff(55,plain,
% 0.55/0.59 (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.55/0.59 tff(56,plain,
% 0.55/0.59 (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.55/0.59 tff(57,plain,
% 0.55/0.59 (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.55/0.59 tff(58,plain,
% 0.55/0.59 (~?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.55/0.59 tff(59,plain,
% 0.55/0.59 (~?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[58, 49])).
% 0.55/0.59 tff(60,plain,
% 0.55/0.59 (~?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.55/0.59 tff(61,plain,
% 0.55/0.59 (~?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[60, 49])).
% 0.55/0.59 tff(62,plain,
% 0.55/0.59 (^[W0: $i] : nnf_neg(refl($oeq((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))), (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))), refl($oeq((~(~(W0 = sz00))), (~(~(W0 = sz00))))), sk($oeq((~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)))))), (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00)))))))), $oeq((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))), ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~(~(W0 = sz00))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00)))))))))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(63,plain,(
% 0.55/0.59 ![W0: $i] : ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~(~(W0 = sz00))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00)))))))),
% 0.55/0.59 inference(nnf-neg,[status(sab)],[61, 62])).
% 0.55/0.59 tff(64,plain,
% 0.55/0.59 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_22(W0) = sz00)))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[63, 48])).
% 0.55/0.59 tff(65,plain,
% 0.55/0.59 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[64, 46])).
% 0.55/0.59 tff(66,plain,
% 0.55/0.59 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[65, 44])).
% 0.55/0.59 tff(67,plain,
% 0.55/0.59 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | ((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | (W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(68,plain,
% 0.55/0.59 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | ((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 0.55/0.59 inference(quant_inst,[status(thm)],[])).
% 0.55/0.59 tff(69,plain,
% 0.55/0.59 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))) | (W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.55/0.59 tff(70,plain,
% 0.55/0.59 (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.55/0.59 inference(unit_resolution,[status(thm)],[69, 66, 42, 40])).
% 0.55/0.59 tff(71,plain,
% 0.55/0.59 (((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))) | aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 0.55/0.59 inference(tautology,[status(thm)],[])).
% 0.55/0.59 tff(72,plain,
% 0.55/0.59 (aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 0.55/0.59 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.55/0.59 tff(73,plain,
% 0.55/0.59 (((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))) | (~(tptp_fun_W1_22(W1!21) = sz00))),
% 0.55/0.59 inference(tautology,[status(thm)],[])).
% 0.55/0.59 tff(74,plain,
% 0.55/0.59 (~(tptp_fun_W1_22(W1!21) = sz00)),
% 0.55/0.59 inference(unit_resolution,[status(thm)],[73, 70])).
% 0.55/0.59 tff(75,plain,
% 0.55/0.59 (((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))) | iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))),
% 0.55/0.59 inference(tautology,[status(thm)],[])).
% 0.55/0.59 tff(76,plain,
% 0.55/0.59 (iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))),
% 0.55/0.59 inference(unit_resolution,[status(thm)],[75, 70])).
% 0.55/0.59 tff(77,plain,
% 0.55/0.59 (((W1!21 = sz00) | (~aElementOf0(W1!21, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) | ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.55/0.59 inference(tautology,[status(thm)],[])).
% 0.55/0.59 tff(78,plain,
% 0.55/0.59 (![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.55/0.59 inference(unit_resolution,[status(thm)],[77, 38])).
% 0.55/0.59 tff(79,plain,
% 0.55/0.59 (((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | ((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) <=> ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(80,plain,
% 0.55/0.59 (((tptp_fun_W1_22(W1!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))) <=> ((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(81,plain,
% 0.55/0.59 (((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | ((tptp_fun_W1_22(W1!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) <=> ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | ((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))),
% 0.55/0.59 inference(monotonicity,[status(thm)],[80])).
% 0.55/0.59 tff(82,plain,
% 0.55/0.59 (((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | ((tptp_fun_W1_22(W1!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) <=> ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.55/0.59 inference(transitivity,[status(thm)],[81, 79])).
% 0.55/0.59 tff(83,plain,
% 0.55/0.59 ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | ((tptp_fun_W1_22(W1!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 0.55/0.59 inference(quant_inst,[status(thm)],[])).
% 0.55/0.59 tff(84,plain,
% 0.55/0.59 ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.55/0.59 tff(85,plain,
% 0.55/0.59 ($false),
% 0.55/0.59 inference(unit_resolution,[status(thm)],[84, 78, 76, 74, 72])).
% 0.55/0.59 % SZS output end Proof
%------------------------------------------------------------------------------