TSTP Solution File: COL106-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL106-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 6 17:48:38 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL106-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 12:35:35 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(c_in_type, type, (
% 0.20/0.40 c_in: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(tc_prod_type, type, (
% 0.20/0.40 tc_prod: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tc_Comb_Ocomb_type, type, (
% 0.20/0.40 tc_Comb_Ocomb: $i)).
% 0.20/0.40 tff(c_Comb_Oparcontract_type, type, (
% 0.20/0.40 c_Comb_Oparcontract: $i)).
% 0.20/0.40 tff(c_Pair_type, type, (
% 0.20/0.40 c_Pair: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.40 tff(v_sko__uTE_type, type, (
% 0.20/0.40 v_sko__uTE: ( $i * $i ) > $i)).
% 0.20/0.40 tff(v_sko__uTI_type, type, (
% 0.20/0.40 v_sko__uTI: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(v_xb_type, type, (
% 0.20/0.40 v_xb: $i)).
% 0.20/0.40 tff(v_ya_type, type, (
% 0.20/0.40 v_ya: $i)).
% 0.20/0.40 tff(c_Comb_Ocomb_Oop_A_D_D_type, type, (
% 0.20/0.40 c_Comb_Ocomb_Oop_A_D_D: ( $i * $i ) > $i)).
% 0.20/0.40 tff(v_x_type, type, (
% 0.20/0.40 v_x: $i)).
% 0.20/0.40 tff(c_Comb_Ocomb_OK_type, type, (
% 0.20/0.40 c_Comb_Ocomb_OK: $i)).
% 0.20/0.40 tff(v_sko__uTH_type, type, (
% 0.20/0.40 v_sko__uTH: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(v_sko__uTG_type, type, (
% 0.20/0.40 v_sko__uTG: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(v_sko__uTF_type, type, (
% 0.20/0.40 v_sko__uTF: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(c_Comb_Ocomb_OS_type, type, (
% 0.20/0.40 c_Comb_Ocomb_OS: $i)).
% 0.20/0.40 tff(1,assumption,(v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb) = c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_x, tc_Comb_Ocomb, tc_Comb_Ocomb)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(symmetry,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (^[V_x: $i, V_y: $i] : refl(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> ![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> ![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(8,axiom,(![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Oparcontract_Ointros__2_0')).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.40 tff(10,plain,(
% 0.20/0.40 ![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(skolemize,[status(sab)],[9])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 ((~![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.20/0.40 tff(15,assumption,(~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), introduced(assumption)).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (^[V_x: $i] : refl(c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> ![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> ![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(19,axiom,(![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Oparcontract_Ointros__1_0')).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.40 tff(21,plain,(
% 0.20/0.40 ![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(skolemize,[status(sab)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((~![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[23, 22, 15])).
% 0.20/0.40 tff(25,plain,(c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (^[V_U: $i] : refl(((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (^[V_U: $i] : rewrite(((~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![V_U: $i] : ((~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.40 tff(31,axiom,(![V_U: $i] : ((~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.40 tff(34,plain,(
% 0.20/0.40 ![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[33])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) <=> ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (~c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 35, 25])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[39, 14])).
% 0.20/0.41 tff(41,plain,(~(v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(42,assumption,(v_x = v_xb), introduced(assumption)).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (v_xb = v_x),
% 0.20/0.41 inference(symmetry,[status(thm)],[42])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb) = c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.41 inference(symmetry,[status(thm)],[45])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (c_in(c_Pair(v_xb, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[25, 46])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[39, 47])).
% 0.20/0.41 tff(49,plain,(~(v_x = v_xb)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(50,assumption,(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)), introduced(assumption)).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (^[V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : refl(((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H)) <=> ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H)) <=> ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H)) <=> ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(54,axiom,(![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Ocomb_Oinject__iff1_1')).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.41 tff(56,plain,(
% 0.20/0.41 ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))),
% 0.20/0.41 inference(skolemize,[status(sab)],[55])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))) | (v_x = v_xb))) <=> ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))) | (v_x = v_xb))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))) | (v_x = v_xb))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))) | (v_x = v_xb)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[60, 57, 50, 49])).
% 0.20/0.41 tff(62,plain,(~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(63,assumption,(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), introduced(assumption)).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (^[V_comb1_H: $i, V_comb2_H: $i] : refl((~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) <=> (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) <=> ![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) <=> ![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(67,axiom,(![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Ocomb_Odistinct__3__iff1_0')).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.41 tff(69,plain,(
% 0.20/0.41 ![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[68])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 ((~![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))) | (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[71, 70, 63])).
% 0.20/0.41 tff(73,plain,(~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(74,assumption,(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), introduced(assumption)).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (^[V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : refl(((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H)) <=> ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H)) <=> ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H)) <=> ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(78,axiom,(![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Ocomb_Oinject__iff1_0')).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.41 tff(80,plain,(
% 0.20/0.41 ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))),
% 0.20/0.41 inference(skolemize,[status(sab)],[79])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))) | ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))) | (c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))) <=> ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))) | (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))) | (c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))) | ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))) | (c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))) | (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))) | (c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[84, 81, 74, 73])).
% 0.20/0.41 tff(86,plain,(~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (^[V_q: $i, V_r: $i, V_p: $i] : refl(((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (^[V_q: $i, V_r: $i, V_p: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> (((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))))), rewrite((((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))), ((((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r)))) <=> (((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r)))))), rewrite((((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r)))) <=> ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), ((((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r)))) <=> ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (![V_q: $i, V_r: $i, V_p: $i] : (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r)))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.42 tff(92,axiom,(![V_q: $i, V_r: $i, V_p: $i] : (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_OAp__parcontractE_0')).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.42 tff(95,plain,(
% 0.20/0.42 ![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[94])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(98,axiom,(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (((~![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) <=> ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[102, 99, 96])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 ((v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[103, 86])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[104, 62, 41])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)) = v_xb),
% 0.20/0.42 inference(symmetry,[status(thm)],[105])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (^[V_q: $i, V_r: $i, V_p: $i] : refl(((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (^[V_q: $i, V_r: $i, V_p: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) <=> ((V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) <=> (((V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))))), rewrite((((V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), ((((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> (((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))))), rewrite((((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), ((((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (![V_q: $i, V_r: $i, V_p: $i] : (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.43 tff(112,axiom,(![V_q: $i, V_r: $i, V_p: $i] : (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_OAp__parcontractE_2')).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.20/0.43 tff(115,plain,(
% 0.20/0.43 ![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[114])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (((~![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | ((c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | ((c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 ((c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[119, 99, 116])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 ((c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[120, 86])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[121, 62, 41])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (^[V_x: $i, V_z: $i] : refl(((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z)))) <=> ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z)))) <=> ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z)))) <=> ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(126,axiom,(![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_OK1__parcontractD__dest_0')).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.44 tff(128,plain,(
% 0.20/0.44 ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[127])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))))) <=> ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[132, 129, 122])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) = v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)),
% 0.20/0.44 inference(symmetry,[status(thm)],[133])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)) = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)) = v_xb),
% 0.20/0.44 inference(transitivity,[status(thm)],[135, 106])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb) = c_Pair(v_xb, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(v_xb, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[137])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 (c_in(c_Pair(v_xb, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.44 inference(symmetry,[status(thm)],[138])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 ((~c_in(c_Pair(v_xb, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (^[V_x: $i, V_z: $i] : refl(((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(144,axiom,(![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_OK1__parcontractD__dest_1')).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.45 tff(146,plain,(
% 0.20/0.45 ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[145])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_x, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_x, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_x, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_x, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 (c_in(c_Pair(v_x, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[150, 147, 122])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((~c_in(c_Pair(v_x, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) <=> ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (~c_in(c_Pair(v_x, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((~c_in(c_Pair(v_x, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (~c_in(c_Pair(v_x, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (~c_in(c_Pair(v_xb, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[154, 35, 151])).
% 0.20/0.46 tff(156,plain,
% 0.20/0.46 (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[155, 140])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 ((~![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_x, v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[157, 11])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[158, 156])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------