%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL106-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 01:02:53 PM UTC 2026
% Result : Unsatisfiable 21.27s 5.17s
% Output : CNFRefutation 21.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 13 unt; 0 def)
% Number of atoms : 138 ( 84 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 129 ( 45 ~; 84 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 87 ( 0 sgn 87 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(v_x,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_xb,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X2 = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(X0,X1,X2),v_sko__uTH(X0,X1,X2))
| X0 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X0,X1,X2)),v_sko__uTG(X0,X1,X2))
| X0 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)
| X2 = c_Comb_Ocomb_Oop_A_D_D(X0,X1)
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X0,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OAp__parcontractE_0) ).
fof(f4,plain,
! [X2,X0,X1] :
( c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(X0,X1,X2),v_sko__uTH(X0,X1,X2)) = X2
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X0,X1,X2)),v_sko__uTG(X0,X1,X2)) = X0
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2) = X0
| c_Comb_Ocomb_Oop_A_D_D(X0,X1) = X2
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X0,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( X0 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X0,X1,X2)),v_sko__uTG(X0,X1,X2))
| X0 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)
| X2 = c_Comb_Ocomb_Oop_A_D_D(X0,X1)
| c_in(c_Pair(X0,v_sko__uTI(X0,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(X0,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OAp__parcontractE_2) ).
fof(f6,plain,
! [X2,X0,X1] :
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X0,X1,X2)),v_sko__uTG(X0,X1,X2)) = X0
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2) = X0
| c_Comb_Ocomb_Oop_A_D_D(X0,X1) = X2
| c_in(c_Pair(X0,v_sko__uTI(X0,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(X0,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0,X1] : c_Comb_Ocomb_OK != c_Comb_Ocomb_Oop_A_D_D(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocomb_Odistinct__3__iff1_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Comb_Ocomb_Oop_A_D_D(X0,X1) != c_Comb_Ocomb_Oop_A_D_D(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_0) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( X1 = X3
| c_Comb_Ocomb_Oop_A_D_D(X0,X1) != c_Comb_Ocomb_Oop_A_D_D(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_1) ).
fof(f10,axiom,
! [X0,X1] :
( X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X0,X1))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OK1__parcontractD__dest_0) ).
fof(f11,plain,
! [X0,X1] :
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X0,X1)) = X1
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( c_in(c_Pair(X0,v_sko__uTE(X0,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,X0),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OK1__parcontractD__dest_1) ).
fof(f13,axiom,
! [X0] : c_in(c_Pair(X0,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__1_0) ).
fof(f14,axiom,
! [X0,X1] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1),X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__2_0) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__4_0) ).
tcf(c_61,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)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( ~ c_in(c_Pair(v_xb,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_x,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2) = X0 )
| ( c_Comb_Ocomb_Oop_A_D_D(X0,X1) = X2 )
| ( c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(X0,X1,X2),v_sko__uTH(X0,X1,X2)) = X2 )
| ( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X0,X1,X2)),v_sko__uTG(X0,X1,X2)) = X0 )
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X0,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,v_sko__uTI(X0,X1,X2),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,X2) = X0 )
| ( c_Comb_Ocomb_Oop_A_D_D(X0,X1) = X2 )
| ( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X0,X1,X2)),v_sko__uTG(X0,X1,X2)) = X0 )
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X0,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : c_Comb_Ocomb_Oop_A_D_D(X0,X1) != c_Comb_Ocomb_OK,
inference(cnf_transformation,[],[f7]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( c_Comb_Ocomb_Oop_A_D_D(X0,X1) != c_Comb_Ocomb_Oop_A_D_D(X2,X3) ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( c_Comb_Ocomb_Oop_A_D_D(X0,X1) != c_Comb_Ocomb_Oop_A_D_D(X2,X3) ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X0,X1)) = X1 )
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( c_in(c_Pair(X0,v_sko__uTE(X0,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,X0),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_70,plain,
! [X0: $i] : 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,[],[f13]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1),X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,[],[f15]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Comb_Ocomb_Oop_A_D_D(X0,X1) = c_Comb_Ocomb_OK )
| ( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(X0,X1),X2) != c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X3) ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_443,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) )
| ( 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(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_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) ) ),
inference(superposition,[status(thm)],[c_61,c_63]) ).
tcf(c_576,plain,
( ( 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)) = c_Comb_Ocomb_OK )
| ( 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) ) ),
inference(instantiation,[status(thm)],[c_402]) ).
tcf(c_766,plain,
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)) != c_Comb_Ocomb_OK,
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1480,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,v_sko__uTE(X0,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,X2)),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,X0) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2) )
| ( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1) = X2 )
| ( 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,X0),X1,X2)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,X2)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0) )
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(superposition,[status(thm)],[c_64,c_69]) ).
tcf(c_1481,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2) )
| ( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1) = X2 )
| ( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X0,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,X2))) = v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,X2) )
| ( 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,X0),X1,X2)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,X2)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0) )
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(superposition,[status(thm)],[c_64,c_68]) ).
tcf(c_1503,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) )
| ( 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_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_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) ) ),
inference(superposition,[status(thm)],[c_61,c_1481]) ).
tcf(c_1510,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) )
| ( 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_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) ) ),
inference(global_subsumption_just,[status(thm)],[c_1503,c_576,c_766,c_1503]) ).
tcf(c_1524,plain,
! [X0: $i] :
( 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),X0),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_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) )
| ( 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(superposition,[status(thm)],[c_1510,c_71]) ).
tcf(c_1571,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,v_sko__uTE(X0,c_Comb_Ocomb_Oop_A_D_D(X2,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_OK,X2,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(superposition,[status(thm)],[c_72,c_69]) ).
tcf(c_1582,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) )
| ( 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(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_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) ) ),
inference(superposition,[status(thm)],[c_61,c_63]) ).
tcf(c_1675,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) )
| ( 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(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 ) ),
inference(global_subsumption_just,[status(thm)],[c_1582,c_443,c_576,c_766]) ).
tcf(c_1691,plain,
( 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_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) )
| ( 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(superposition,[status(thm)],[c_1675,c_1524]) ).
tcf(c_1723,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) )
| ( 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_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(superposition,[status(thm)],[c_1691,c_62]) ).
tcf(c_1727,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) )
| ( 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_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_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)) ),
inference(superposition,[status(thm)],[c_1480,c_1723]) ).
tcf(c_1728,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) )
| ( 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_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) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1727,c_61]) ).
tcf(c_1729,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) )
| ( 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(global_subsumption_just,[status(thm)],[c_1728,c_576,c_766,c_1728]) ).
tcf(c_1745,plain,
( 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_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(superposition,[status(thm)],[c_1729,c_71]) ).
tcf(c_1757,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) )
| ~ 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(superposition,[status(thm)],[c_1745,c_62]) ).
tcf(c_1758,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(forward_subsumption_resolution,[status(thm)],[c_1757,c_70]) ).
tcf(c_1769,plain,
! [X0: $i,X1: $i] :
( ( X1 = v_xb )
| ( c_Comb_Ocomb_Oop_A_D_D(X0,X1) != c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) ) ),
inference(superposition,[status(thm)],[c_1758,c_67]) ).
tcf(c_1802,plain,
v_x = v_xb,
inference(equality_resolution,[status(thm)],[c_1769]) ).
tcf(c_1813,plain,
! [X0: $i,X1: $i] :
( ~ 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(c_Comb_Ocomb_OK,X0,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_xb,c_Comb_Ocomb_Oop_A_D_D(X0,X1)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(superposition,[status(thm)],[c_1571,c_62]) ).
tcf(c_1840,plain,
! [X0: $i,X1: $i] :
( ~ c_in(c_Pair(v_x,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_OK,X0,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,c_Comb_Ocomb_Oop_A_D_D(X0,X1)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(light_normalisation,[status(thm)],[c_1813,c_1802]) ).
tcf(c_1844,plain,
! [X0: $i,X1: $i] :
( ~ c_in(c_Pair(v_x,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_OK,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1840,c_1571]) ).
tcf(c_1850,plain,
! [X0: $i] : ~ c_in(c_Pair(v_x,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(superposition,[status(thm)],[c_70,c_1844]) ).
tcf(c_1855,plain,
$false,
inference(superposition,[status(thm)],[c_70,c_1850]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL106-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Fri Sep 25 07:36:20 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.33
% 0.04/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.33
% 0.04/0.33 % Detected problem language: tptp
% 0.08/0.34 % Proving...
% 21.27/5.17 % SZS status Started for theBenchmark.p
% 21.27/5.17 % SZS status Unsatisfiable for theBenchmark.p
% 21.27/5.17
% 21.27/5.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.27/5.17
% 21.27/5.17 % ------ iProver source info
% 21.27/5.17
% 21.27/5.17 % git: date: 2026-07-19 20:42:38 +0200
% 21.27/5.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.27/5.17 % git: non_committed_changes: false
% 21.27/5.17
% 21.27/5.17 % ------ Parsing...% successful
% 21.27/5.17
% 21.27/5.17
% 21.27/5.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.27/5.17
% 21.27/5.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 21.27/5.17
% 21.27/5.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.27/5.17
% 21.27/5.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 21.27/5.17 % ------ Proving...
% 21.27/5.17 % ------ Problem Properties
% 21.27/5.17
% 21.27/5.17 %
% 21.27/5.17 % clauses 12
% 21.27/5.17 % conjectures 2
% 21.27/5.17 % EPR 0
% 21.27/5.17 % Horn 10
% 21.27/5.17 % unary 4
% 21.27/5.17 % binary 5
% 21.27/5.17 % lits 27
% 21.27/5.17 % lits eq 13
% 21.27/5.17 % fd_pure 0
% 21.27/5.17 % fd_pseudo 0
% 21.27/5.17 % fd_cond 0
% 21.27/5.17 % fd_pseudo_cond 2
% 21.27/5.17 % AC symbols 0
% 21.27/5.17
% 21.27/5.17 % ------ Input Options Time Limit: Unbounded
% 21.27/5.17
% 21.27/5.17
% 21.27/5.17 % ------
% 21.27/5.17 % Current options:
% 21.27/5.17 % ------
% 21.27/5.17
% 21.27/5.17
% 21.27/5.17 %
% 21.27/5.17
% 21.27/5.17 % ------ Proving...
% 21.27/5.17 %
% 21.27/5.17
% 21.27/5.17 % SZS status Unsatisfiable for theBenchmark.p
% 21.27/5.17
% 21.27/5.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.27/5.17
% 21.27/5.17
%------------------------------------------------------------------------------