%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL106-2 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.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 May 5 04:12:22 PM UTC 2026
% Result : Unsatisfiable 49.45s 31.18s
% Output : CNFRefutation 49.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of clauses : 62 ( 18 unt; 20 nHn; 52 RR)
% Number of literals : 147 ( 98 equ; 48 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 99 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Comb_OAp__parcontractE_2,axiom,
( c_in(c_Pair(X1,v_sko__uTI(X1,X2,X3),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| X3 = c_Comb_Ocomb_Oop_A_D_D(X1,X2)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X3)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X1,X2,X3)),v_sko__uTG(X1,X2,X3))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X2),X3,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_OAp__parcontractE_2) ).
cnf(cls_conjecture_0,negated_conjecture,
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) ).
cnf(cls_Comb_OK1__parcontractD__dest_0,axiom,
( X2 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,X2))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2,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_0) ).
cnf(cls_Comb_Ocomb_Oinject__iff1_0,axiom,
( X1 = X3
| c_Comb_Ocomb_Oop_A_D_D(X1,X2) != c_Comb_Ocomb_Oop_A_D_D(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_0) ).
cnf(cls_Comb_OAp__parcontractE_0,axiom,
( X3 = c_Comb_Ocomb_Oop_A_D_D(X1,X2)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X3)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X1,X2,X3)),v_sko__uTG(X1,X2,X3))
| X3 = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(X1,X2,X3),v_sko__uTH(X1,X2,X3))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X2),X3,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_OAp__parcontractE_0) ).
cnf(cls_Comb_Ocomb_Odistinct__3__iff1_0,axiom,
c_Comb_Ocomb_OK != c_Comb_Ocomb_Oop_A_D_D(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Odistinct__3__iff1_0) ).
cnf(cls_Comb_Oparcontract_Ointros__2_0,axiom,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2),X1,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) ).
cnf(cls_Comb_OK1__parcontractD__dest_1,axiom,
( c_in(c_Pair(X1,v_sko__uTE(X1,X2),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,X1),X2,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) ).
cnf(cls_Comb_Oparcontract_Ointros__4_0,axiom,
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X3,X1),c_Comb_Ocomb_Oop_A_D_D(X4,X2),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X3,X4,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__4_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ c_in(c_Pair(v_xb,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_x,X1,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) ).
cnf(cls_Comb_Oparcontract_Ointros__1_0,axiom,
c_in(c_Pair(X1,X1,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) ).
cnf(cls_Comb_Ocomb_Oinject__iff1_1,axiom,
( X2 = X4
| c_Comb_Ocomb_Oop_A_D_D(X1,X2) != c_Comb_Ocomb_Oop_A_D_D(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_1) ).
cnf(c_0_12,axiom,
( c_in(c_Pair(X1,v_sko__uTI(X1,X2,X3),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| X3 = c_Comb_Ocomb_Oop_A_D_D(X1,X2)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X3)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X1,X2,X3)),v_sko__uTG(X1,X2,X3))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X2),X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_Comb_OAp__parcontractE_2 ).
cnf(c_0_13,negated_conjecture,
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)),
cls_conjecture_0 ).
cnf(c_0_14,axiom,
( X2 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,X2))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_Comb_OK1__parcontractD__dest_0 ).
cnf(c_0_15,negated_conjecture,
( 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_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_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| 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)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
( X1 = X3
| c_Comb_Ocomb_Oop_A_D_D(X1,X2) != c_Comb_Ocomb_Oop_A_D_D(X3,X4) ),
cls_Comb_Ocomb_Oinject__iff1_0 ).
cnf(c_0_17,negated_conjecture,
( 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_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)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,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_OK,v_x),v_ya) = v_xb ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
( X3 = c_Comb_Ocomb_Oop_A_D_D(X1,X2)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X3)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X1,X2,X3)),v_sko__uTG(X1,X2,X3))
| X3 = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(X1,X2,X3),v_sko__uTH(X1,X2,X3))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X2),X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_Comb_OAp__parcontractE_0 ).
cnf(c_0_19,negated_conjecture,
( 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)
| 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)) = X1
| c_Comb_Ocomb_Oop_A_D_D(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_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_x) != c_Comb_Ocomb_Oop_A_D_D(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
c_Comb_Ocomb_OK != c_Comb_Ocomb_Oop_A_D_D(X1,X2),
cls_Comb_Ocomb_Odistinct__3__iff1_0 ).
cnf(c_0_21,negated_conjecture,
( 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(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
| c_Comb_Ocomb_Oop_A_D_D(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_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) ),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_22,axiom,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
cls_Comb_Oparcontract_Ointros__2_0 ).
cnf(c_0_23,negated_conjecture,
( 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)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,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_OK,v_x),v_ya) = v_xb ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_19]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( 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
| 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)) = X1
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,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_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(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_25,axiom,
( c_in(c_Pair(X1,v_sko__uTE(X1,X2),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,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_Comb_OK1__parcontractD__dest_1 ).
cnf(c_0_26,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(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_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_in(c_Pair(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),X1),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)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( 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
| c_Comb_Ocomb_Oop_A_D_D(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_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_20]) ).
cnf(c_0_28,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2))) = v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2)
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_14,c_0_25]) ).
cnf(c_0_29,axiom,
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X3,X1),c_Comb_Ocomb_Oop_A_D_D(X4,X2),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X3,X4,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_Comb_Oparcontract_Ointros__4_0 ).
cnf(c_0_30,negated_conjecture,
( ~ c_in(c_Pair(v_xb,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_x,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_conjecture_1 ).
cnf(c_0_31,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,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_OK,v_x),v_ya) = v_xb
| 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)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),c_Comb_Ocomb_Oop_A_D_D(X2,X3)))) = v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),c_Comb_Ocomb_Oop_A_D_D(X2,X3))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_OK,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(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_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| ~ 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)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
c_in(c_Pair(X1,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
cls_Comb_Oparcontract_Ointros__1_0 ).
cnf(c_0_35,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(X2,X3))) = c_Comb_Ocomb_Oop_A_D_D(X2,X3)
| ~ c_in(c_Pair(c_Comb_Ocomb_OK,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X1,X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_14,c_0_29]) ).
cnf(c_0_36,plain,
( c_Comb_Ocomb_OK = X1
| v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2),c_Comb_Ocomb_Oop_A_D_D(X3,X4)) != c_Comb_Ocomb_Oop_A_D_D(X1,X5)
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2),X4,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_OK,X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_16,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,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_OK,v_x),v_ya) = v_xb
| ~ 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)) ),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_38,axiom,
( X2 = X4
| c_Comb_Ocomb_Oop_A_D_D(X1,X2) != c_Comb_Ocomb_Oop_A_D_D(X3,X4) ),
cls_Comb_Ocomb_Oinject__iff1_1 ).
cnf(c_0_39,plain,
c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),
inference(spm,[status(thm)],[c_0_14,c_0_34]) ).
cnf(c_0_40,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)
| ~ c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_41,plain,
( c_Comb_Ocomb_OK = X1
| v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2),c_Comb_Ocomb_Oop_A_D_D(X3,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2))) != c_Comb_Ocomb_Oop_A_D_D(X1,X4)
| ~ c_in(c_Pair(c_Comb_Ocomb_OK,X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( 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_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_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) ),
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_43,plain,
( v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)) = X2
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1) != c_Comb_Ocomb_Oop_A_D_D(X3,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),
inference(spm,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_45,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,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_OK,v_x),v_ya) = v_xb
| v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),c_Comb_Ocomb_Oop_A_D_D(X2,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1))) != c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| ~ c_in(c_Pair(c_Comb_Ocomb_OK,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_20]) ).
cnf(c_0_46,plain,
v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)) = X1,
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_47,plain,
( v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)) = X3
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1) != c_Comb_Ocomb_Oop_A_D_D(X4,X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(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_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,X1) != c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_34]),c_0_46]) ).
cnf(c_0_49,plain,
v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)) = X1,
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,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_OK,v_x),v_ya) = v_xb ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( ~ c_in(c_Pair(v_x,v_sko__uTE(v_xb,X1),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_xb),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_52,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| v_sko__uTE(v_xb,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)) = v_x ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb),
inference(spm,[status(thm)],[c_0_40,c_0_13]) ).
cnf(c_0_54,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34])]) ).
cnf(c_0_55,negated_conjecture,
( v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)) = X1
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) != c_Comb_Ocomb_Oop_A_D_D(X2,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| ~ 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)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_29]),c_0_34])]) ).
cnf(c_0_57,negated_conjecture,
v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)) = v_xb,
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_58,negated_conjecture,
c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_50]),c_0_56]) ).
cnf(c_0_59,negated_conjecture,
~ c_in(c_Pair(v_x,v_xb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
cnf(c_0_60,negated_conjecture,
v_xb = v_x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_49]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : COL106-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Mon May 4 11:17:27 EDT 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 49.45/31.18 % Version : CSE_E---1.7
% 49.45/31.18 % Problem : theBenchmark.p
% 49.45/31.18 % SZS status Unsatisfiable for theBenchmark.p
% 49.45/31.18 % SZS output start CNFRefutation
% See solution above
% 49.64/31.37 % Total time : 22.387s
%------------------------------------------------------------------------------