%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL124-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 : Sat Jun 21 05:00:53 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : COL124-2 : TPTP v9.0.0. Released v3.2.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 12:19:11 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(c_in_type, type, (
% 0.14/0.41 c_in: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(tc_prod_type, type, (
% 0.14/0.41 tc_prod: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tc_Comb_Ocomb_type, type, (
% 0.14/0.41 tc_Comb_Ocomb: $i)).
% 0.14/0.41 tff(c_Comb_Ocontract_type, type, (
% 0.14/0.41 c_Comb_Ocontract: $i)).
% 0.14/0.41 tff(c_Pair_type, type, (
% 0.14/0.41 c_Pair: ( $i * $i * $i * $i ) > $i)).
% 0.14/0.41 tff(v_x_type, type, (
% 0.14/0.41 v_x: ( $i * $i * $i ) > $i)).
% 0.14/0.41 tff(c_Comb_OI_type, type, (
% 0.14/0.41 c_Comb_OI: $i)).
% 0.14/0.41 tff(c_Comb_Ocomb_Oop_A_D_D_type, type, (
% 0.14/0.41 c_Comb_Ocomb_Oop_A_D_D: ( $i * $i ) > $i)).
% 0.14/0.41 tff(elem_0_type, type, (
% 0.14/0.41 elem_0: $i)).
% 0.14/0.41 tff(c_Comb_Ocomb_OK_type, type, (
% 0.14/0.41 c_Comb_Ocomb_OK: $i)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 (^[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_Ocontract, 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_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (![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_Ocontract, 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_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (![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_Ocontract, 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_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(4,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_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Ocontract_OK_0')).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (![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_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.41 tff(6,plain,(
% 0.14/0.41 ![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_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.14/0.41 inference(skolemize,[status(sab)],[5])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (![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_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 ((~![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_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (^[V_W: $i, V_V: $i, V_U: $i] : refl(((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (^[V_W: $i, V_V: $i, V_U: $i] : trans(monotonicity(rewrite((c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), (((c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> (((~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))), rewrite((((~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), (((c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(14,plain,
% 0.14/0.42 (![V_W: $i, V_V: $i, V_U: $i] : ((c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.14/0.42 tff(15,axiom,(![V_W: $i, V_V: $i, V_U: $i] : ((c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.14/0.42 tff(16,plain,
% 0.14/0.42 (![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.14/0.42 tff(17,plain,
% 0.14/0.42 (![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.14/0.42 tff(18,plain,(
% 0.14/0.42 ![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[17])).
% 0.14/0.42 tff(19,plain,
% 0.14/0.42 (![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.14/0.42 tff(20,plain,
% 0.14/0.42 (((~![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(21,plain,
% 0.14/0.42 (((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(22,plain,
% 0.14/0.42 (((~![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[21])).
% 0.14/0.42 tff(23,plain,
% 0.14/0.42 (((~![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.42 inference(transitivity,[status(thm)],[22, 20])).
% 0.14/0.42 tff(24,plain,
% 0.14/0.42 ((~![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(25,plain,
% 0.14/0.42 ((~![V_W: $i, V_V: $i, V_U: $i] : ((~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, 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, c_Comb_OI), elem!0), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.14/0.43 tff(26,plain,
% 0.14/0.43 (c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[25, 19, 9])).
% 0.14/0.43 tff(27,plain,
% 0.14/0.43 (^[V_z: $i] : refl((~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> (~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(28,plain,
% 0.14/0.43 (![V_z: $i] : (~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_z: $i] : (~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[27])).
% 0.14/0.43 tff(29,plain,
% 0.14/0.43 (![V_z: $i] : (~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_z: $i] : (~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(30,axiom,(![V_z: $i] : (~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_OI__contract__E_0')).
% 0.14/0.43 tff(31,plain,
% 0.14/0.43 (![V_z: $i] : (~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.14/0.43 tff(32,plain,(
% 0.14/0.43 ![V_z: $i] : (~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.43 inference(skolemize,[status(sab)],[31])).
% 0.14/0.43 tff(33,plain,
% 0.14/0.43 (![V_z: $i] : (~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.14/0.43 tff(34,plain,
% 0.14/0.43 ((~![V_z: $i] : (~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), elem!0), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(35,plain,
% 0.14/0.43 ($false),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[34, 33, 26])).
% 0.14/0.43 % SZS output end Proof
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------