%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL118-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:02:07 PM UTC 2026
% Result : Unsatisfiable 5.96s 1.29s
% Output : Proof 5.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 48 unt; 0 def)
% Number of atoms : 68 ( 37 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 23 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 60 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,negated_conjecture,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),V_U,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_x,v_z),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_2) ).
fof(f2_nnf,plain,
! [V_U] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),V_U,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_x,v_z),V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_U] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),V_U,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_x,v_z),V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),X0,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_x,v_z),X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t4,plain,
ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t17,plain,
ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,true),true) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f4,axiom,
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x,V_z),c_Comb_Ocomb_Oop_A_D_D(V_y,V_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(V_x,V_y,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(V_z,V_w,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) ).
fof(f4_nnf,plain,
! [V_z,V_w,V_x,V_y] :
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x,V_z),c_Comb_Ocomb_Oop_A_D_D(V_y,V_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(V_x,V_y,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(V_z,V_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_z,V_w,V_x,V_y] :
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x,V_z),c_Comb_Ocomb_Oop_A_D_D(V_y,V_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(V_x,V_y,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(V_z,V_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X2,X0),c_Comb_Ocomb_Oop_A_D_D(X3,X1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X2,X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X0,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t5,plain,
ifeq(c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,ifeq(c_in(c_Pair(X3,X4,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,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)),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t10,plain,
ifeq(c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,ifeq(c_in(c_Pair(X3,X4,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,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)),true),true) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f3,axiom,
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) ).
fof(f3_nnf,plain,
! [V_x] : 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(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_x] : 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(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
c_in(c_Pair(X0,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t1,plain,
c_in(c_Pair(X1,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t7,plain,
c_in(c_Pair(X1,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t11,plain,
true = ifeq(true,true,ifeq(c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X3),c_Comb_Ocomb_Oop_A_D_D(X2,X3),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true),true),
inference(cp,[status(thm)],[t10,t7]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t91,plain,
true = ifeq(c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X3),c_Comb_Ocomb_Oop_A_D_D(X2,X3),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true),
inference(step,[status(thm)],[t11,t6]) ).
cnf(t22,plain,
ifeq(c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X3),c_Comb_Ocomb_Oop_A_D_D(X2,X3),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true) = true,
inference(orient,[status(thm)],[t91]) ).
cnf(f0,negated_conjecture,
c_in(c_Pair(v_x,v_ya,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) ).
fof(f0_nnf,plain,
c_in(c_Pair(v_x,v_ya,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_in(c_Pair(v_x,v_ya,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(t2,plain,
c_in(c_Pair(v_x,v_ya,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t8,plain,
c_in(c_Pair(v_x,v_ya,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t24,plain,
true = ifeq(true,true,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,X1),c_Comb_Ocomb_Oop_A_D_D(v_ya,X1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true),
inference(cp,[status(thm)],[t22,t8]) ).
cnf(t93,plain,
true = c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,X1),c_Comb_Ocomb_Oop_A_D_D(v_ya,X1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(step,[status(thm)],[t24,t6]) ).
cnf(t29,plain,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,X1),c_Comb_Ocomb_Oop_A_D_D(v_ya,X1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) = true,
inference(orient,[status(thm)],[t93]) ).
cnf(t33,plain,
true = ifeq(true,true,ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,true),true),
inference(cp,[status(thm)],[t17,t29]) ).
cnf(t96,plain,
true = ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,true),
inference(step,[status(thm)],[t33,t6]) ).
cnf(t42,plain,
ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,true) = true,
inference(orient,[status(thm)],[t96]) ).
cnf(f1,negated_conjecture,
c_in(c_Pair(v_z,v_w,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) ).
fof(f1_nnf,plain,
c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(t3,plain,
c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t9,plain,
c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t12,plain,
true = ifeq(true,true,ifeq(c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,v_z),c_Comb_Ocomb_Oop_A_D_D(X2,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true),true),
inference(cp,[status(thm)],[t10,t9]) ).
cnf(t101,plain,
true = ifeq(c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,v_z),c_Comb_Ocomb_Oop_A_D_D(X2,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true),
inference(step,[status(thm)],[t12,t6]) ).
cnf(t59,plain,
ifeq(c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,v_z),c_Comb_Ocomb_Oop_A_D_D(X2,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true) = true,
inference(orient,[status(thm)],[t101]) ).
cnf(t69,plain,
true = ifeq(true,true,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_z),c_Comb_Ocomb_Oop_A_D_D(v_w,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true),
inference(cp,[status(thm)],[t59,t9]) ).
cnf(t103,plain,
true = c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_z),c_Comb_Ocomb_Oop_A_D_D(v_w,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(step,[status(thm)],[t69,t6]) ).
cnf(t77,plain,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_z),c_Comb_Ocomb_Oop_A_D_D(v_w,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) = true,
inference(orient,[status(thm)],[t103]) ).
cnf(t70,plain,
true = ifeq(true,true,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true),
inference(cp,[status(thm)],[t59,t8]) ).
cnf(t104,plain,
true = c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(step,[status(thm)],[t70,t6]) ).
cnf(t82,plain,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) = true,
inference(orient,[status(thm)],[t104]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,true)),
inference(rw,[status(thm)],[g0_0,t42]) ).
cnf(g0_2,plain,
true != ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_z),c_Comb_Ocomb_Oop_A_D_D(v_w,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)))),
inference(rw,[status(thm)],[g0_1,t77]) ).
cnf(g0_3,plain,
true != ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),true,false,ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),c_Comb_Ocomb_Oop_A_D_D(v_ya,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(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),false,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_z),c_Comb_Ocomb_Oop_A_D_D(v_w,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)))),
inference(rw,[status(thm)],[g0_2,t82]) ).
cnf(g0_4,plain,
true != ifeq(true,true,false,ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),c_Comb_Ocomb_Oop_A_D_D(v_ya,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(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),false,c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_z),c_Comb_Ocomb_Oop_A_D_D(v_w,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)))),
inference(rw,[status(thm)],[g0_3,t82]) ).
cnf(g0_5,plain,
true != false,
inference(rw,[status(thm)],[g0_4,t6]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL118-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 07:45:24 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.96/1.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.96/1.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------