%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN086+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 02:30:00 PM UTC 2026
% Result : Theorem 4.81s 1.28s
% Output : CNFRefutation 4.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 117 ( 42 unt; 0 def)
% Number of atoms : 313 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 363 ( 167 ~; 150 |; 46 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 240 ( 0 sgn 218 !; 22 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ id(X3,X2)
& ~ r3(X0,X1,X3) )
| ( r3(X0,X1,X3)
& id(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_3) ).
fof(f4,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ id(X3,X2)
& ~ r4(X0,X1,X3) )
| ( r4(X0,X1,X3)
& id(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_4) ).
fof(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(f6,axiom,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7) ).
fof(f8,axiom,
! [X0,X1] :
( ( r1(X1)
& r1(X0) )
| ( ~ r1(X1)
& ~ r1(X0) )
| ~ id(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(f10,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( r3(X3,X4,X5)
& r3(X0,X1,X2) )
| ( ~ r3(X3,X4,X5)
& ~ r3(X0,X1,X2) )
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_10) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( r4(X3,X4,X5)
& r4(X0,X1,X2) )
| ( ~ r4(X3,X4,X5)
& ~ r4(X0,X1,X2) )
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_11) ).
fof(f13,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r4(X0,X1,X5)
& r3(X5,X0,X2) )
& ? [X3] :
( ? [X4] :
( r4(X0,X4,X3)
& r2(X1,X4) )
& id(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_2a) ).
fof(f15,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& id(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
fof(f16,axiom,
! [X0] :
? [X1] :
( ? [X3] :
( r1(X3)
& id(X1,X3) )
& ? [X2] :
( r4(X0,X2,X1)
& r1(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).
fof(f19,conjecture,
? [X0] :
( ? [X4] :
( r1(X4)
& id(X0,X4) )
& ? [X1] :
( ? [X3] :
( r4(X3,X1,X0)
& r1(X3) )
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerotimesoneidzero) ).
fof(f20,negated_conjecture,
~ ? [X0] :
( ? [X4] :
( r1(X4)
& id(X0,X4) )
& ? [X1] :
( ? [X3] :
( r4(X3,X1,X0)
& r1(X3) )
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0] :
( ! [X4] :
( ~ r1(X4)
| ~ id(X0,X4) )
| ! [X1] :
( ! [X3] :
( ~ r4(X3,X1,X0)
| ~ r1(X3) )
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f23,plain,
! [X0] :
( r1(sK5(X0))
& id(sK3(X0),sK5(X0))
& r4(X0,sK4(X0),sK3(X0))
& r1(sK4(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0)),skolemize(X3,sK5(X0))],[f16]) ).
fof(f24,plain,
! [X0] :
( r3(X0,sK7(X0),sK6(X0))
& r1(sK7(X0))
& id(sK6(X0),X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0))],[f15]) ).
fof(f25,plain,
! [X1] :
( ( ~ id(X1,sK8)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,sK8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f1]) ).
fof(f27,plain,
! [X0,X1] :
( r4(X0,X1,sK13(X0,X1))
& r3(sK13(X0,X1),X0,sK10(X0,X1))
& r4(X0,sK12(X0,X1),sK11(X0,X1))
& r2(X1,sK12(X0,X1))
& id(sK11(X0,X1),sK10(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X2,sK10(X0,X1)),skolemize(X3,sK11(X0,X1)),skolemize(X4,sK12(X0,X1)),skolemize(X5,sK13(X0,X1))],[f13]) ).
fof(f28,plain,
! [X0,X1,X3] :
( ( ~ id(X3,sK14(X0,X1))
& ~ r4(X0,X1,X3) )
| ( r4(X0,X1,X3)
& id(X3,sK14(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X2,sK14(X0,X1))],[f4]) ).
fof(f30,plain,
! [X0,X1,X3] :
( ( ~ id(X3,sK19(X0,X1))
& ~ r3(X0,X1,X3) )
| ( r3(X0,X1,X3)
& id(X3,sK19(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X2,sK19(X0,X1))],[f3]) ).
fof(f31,plain,
! [X2,X3,X0,X1,X4] :
( ~ r1(X4)
| ~ id(X0,X4)
| ~ r4(X3,X1,X0)
| ~ r1(X3)
| ~ r2(X2,X1)
| ~ r1(X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f33,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f34,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f40,plain,
! [X0] : r1(sK5(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X0] : id(sK3(X0),sK5(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0] : r4(X0,sK4(X0),sK3(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X0] : r1(sK4(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
! [X0] : r3(X0,sK7(X0),sK6(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X0] : r1(sK7(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X0] : id(sK6(X0),X0),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X0,X1] :
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f51,plain,
! [X1] :
( ~ id(X1,sK8)
| r1(X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f54,plain,
! [X1] :
( ~ r1(X1)
| id(X1,sK8) ),
inference(cnf_transformation,[],[f25]) ).
fof(f64,plain,
! [X0,X1] : r4(X0,X1,sK13(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
fof(f65,plain,
! [X0,X1] : r3(sK13(X0,X1),X0,sK10(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
fof(f66,plain,
! [X0,X1] : r4(X0,sK12(X0,X1),sK11(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
fof(f67,plain,
! [X0,X1] : r2(X1,sK12(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
fof(f68,plain,
! [X0,X1] : id(sK11(X0,X1),sK10(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X4,X5] :
( r4(X3,X4,X5)
| ~ r4(X0,X1,X2)
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ),
inference(cnf_transformation,[],[f11]) ).
fof(f76,plain,
! [X3,X0,X1] :
( ~ r4(X0,X1,X3)
| id(X3,sK14(X0,X1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f83,plain,
! [X2,X3,X0,X1,X4,X5] :
( r3(X0,X1,X2)
| ~ r3(X3,X4,X5)
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f84,plain,
! [X2,X3,X0,X1,X4,X5] :
( r3(X3,X4,X5)
| ~ r3(X0,X1,X2)
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f89,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| id(X3,sK19(X0,X1)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ r1(X4)
| ~ r1(X3)
| ~ r1(X0)
| ~ id(X2,X4)
| ~ r2(X3,X1)
| ~ r4(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( id(X2,X1)
| ~ id(X2,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i] : id(X0,X0),
inference(cnf_transformation,[],[f34]) ).
tcf(c_58,plain,
! [X0: $i] : r1(sK4(X0)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_59,plain,
! [X0: $i] : r4(X0,sK4(X0),sK3(X0)),
inference(cnf_transformation,[],[f42]) ).
tcf(c_60,plain,
! [X0: $i] : id(sK3(X0),sK5(X0)),
inference(cnf_transformation,[],[f41]) ).
tcf(c_61,plain,
! [X0: $i] : r1(sK5(X0)),
inference(cnf_transformation,[],[f40]) ).
tcf(c_62,plain,
! [X0: $i] : id(sK6(X0),X0),
inference(cnf_transformation,[],[f46]) ).
tcf(c_63,plain,
! [X0: $i] : r1(sK7(X0)),
inference(cnf_transformation,[],[f45]) ).
tcf(c_64,plain,
! [X0: $i] : r3(X0,sK7(X0),sK6(X0)),
inference(cnf_transformation,[],[f44]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_67,plain,
! [X0: $i] :
( id(X0,sK8)
| ~ r1(X0) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_68,plain,
! [X0: $i] :
( r1(X0)
| ~ id(X0,sK8) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : id(sK11(X0,X1),sK10(X0,X1)),
inference(cnf_transformation,[],[f68]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : r2(X0,sK12(X1,X0)),
inference(cnf_transformation,[],[f67]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : r4(X0,sK12(X0,X1),sK11(X0,X1)),
inference(cnf_transformation,[],[f66]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : r3(sK13(X0,X1),X0,sK10(X0,X1)),
inference(cnf_transformation,[],[f65]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : r4(X0,X1,sK13(X0,X1)),
inference(cnf_transformation,[],[f64]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( r4(X5,X4,X3)
| ~ id(X2,X3)
| ~ id(X1,X4)
| ~ id(X0,X5)
| ~ r4(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( id(X2,sK14(X0,X1))
| ~ r4(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( r3(X5,X4,X3)
| ~ id(X2,X3)
| ~ id(X1,X4)
| ~ id(X0,X5)
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( r3(X5,X4,X3)
| ~ id(X5,X0)
| ~ id(X4,X1)
| ~ id(X3,X2)
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( id(X2,sK19(X0,X1))
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_92,plain,
r1(sK7(sK8)),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_94,plain,
r1(sK4(sK8)),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_95,plain,
id(sK8,sK8),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_96,plain,
id(sK6(sK8),sK8),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_98,plain,
r2(sK8,sK12(sK8,sK8)),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_101,plain,
r4(sK8,sK8,sK13(sK8,sK8)),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_102,plain,
( r1(sK8)
| ~ id(sK8,sK8) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_103,plain,
r3(sK8,sK7(sK8),sK6(sK8)),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_104,plain,
r4(sK8,sK4(sK8),sK3(sK8)),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_107,plain,
id(sK11(sK8,sK8),sK10(sK8,sK8)),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_110,plain,
r3(sK13(sK8,sK8),sK8,sK10(sK8,sK8)),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_111,plain,
r4(sK8,sK12(sK8,sK8),sK11(sK8,sK8)),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_120,plain,
( id(sK8,sK14(sK8,sK8))
| ~ r4(sK8,sK8,sK8) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ r1(X4)
| ~ r1(X2)
| ~ r1(X0)
| ~ id(X3,X4)
| ~ r2(X2,sK12(X1,X2))
| ~ r4(X0,sK12(X1,X2),X3) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_465,plain,
! [X0: $i,X1: $i] :
( id(sK13(X0,X1),sK14(X0,X1))
| ~ r4(X0,X1,sK13(X0,X1)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_466,plain,
( id(sK13(sK8,sK8),sK14(sK8,sK8))
| ~ r4(sK8,sK8,sK13(sK8,sK8)) ),
inference(instantiation,[status(thm)],[c_465]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r4(X3,X1,X2)
| ~ id(X0,X3)
| ~ id(sK3(X0),X2)
| ~ id(sK4(X0),X1)
| ~ r4(X0,sK4(X0),sK3(X0)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_515,plain,
( r4(sK8,sK8,sK8)
| ~ id(sK8,sK8)
| ~ id(sK3(sK8),sK8)
| ~ id(sK4(sK8),sK8)
| ~ r4(sK8,sK4(sK8),sK3(sK8)) ),
inference(instantiation,[status(thm)],[c_514]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r3(X3,X2,X1)
| ~ id(X0,X3)
| ~ id(sK7(X0),X2)
| ~ id(sK6(X0),X1)
| ~ r3(X0,sK7(X0),sK6(X0)) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_527,plain,
( r3(sK8,sK8,sK8)
| ~ id(sK8,sK8)
| ~ id(sK7(sK8),sK8)
| ~ id(sK6(sK8),sK8)
| ~ r3(sK8,sK7(sK8),sK6(sK8)) ),
inference(instantiation,[status(thm)],[c_526]) ).
tcf(c_534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( r3(X3,X4,X2)
| ~ id(X4,X0)
| ~ id(X3,sK13(X0,X1))
| ~ id(X2,sK10(X0,X1))
| ~ r3(sK13(X0,X1),X0,sK10(X0,X1)) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0)
| ~ id(sK11(X0,X1),X2)
| ~ r2(X1,sK12(X0,X1))
| ~ r4(X0,sK12(X0,X1),sK11(X0,X1)) ),
inference(instantiation,[status(thm)],[c_427]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i,X2: $i] :
( id(sK14(X1,X2),X0)
| ~ id(X0,sK14(X1,X2)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_626,plain,
( id(sK14(sK8,sK8),sK8)
| ~ id(sK8,sK14(sK8,sK8)) ),
inference(instantiation,[status(thm)],[c_625]) ).
tcf(c_1003,plain,
! [X0: $i] : id(sK5(X0),sK3(X0)),
inference(superposition,[status(thm)],[c_60,c_51]) ).
tcf(c_1190,plain,
! [X0: $i] :
( id(sK4(X0),sK8)
| ~ r1(sK4(X0)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1191,plain,
( id(sK4(sK8),sK8)
| ~ r1(sK4(sK8)) ),
inference(instantiation,[status(thm)],[c_1190]) ).
tcf(c_1297,plain,
! [X0: $i] :
( id(sK7(X0),sK8)
| ~ r1(sK7(X0)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1298,plain,
( id(sK7(sK8),sK8)
| ~ r1(sK7(sK8)) ),
inference(instantiation,[status(thm)],[c_1297]) ).
tcf(c_1379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( id(sK13(X0,X1),X3)
| ~ id(X2,X3)
| ~ id(sK13(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_1526,plain,
! [X0: $i,X1: $i,X2: $i] :
( id(X2,sK13(X0,X1))
| ~ id(sK13(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1527,plain,
( id(sK8,sK13(sK8,sK8))
| ~ id(sK13(sK8,sK8),sK8) ),
inference(instantiation,[status(thm)],[c_1526]) ).
tcf(c_1836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( id(sK11(X2,X3),sK19(X0,X1))
| ~ r3(X0,X1,sK11(X2,X3)) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_1838,plain,
( id(sK11(sK8,sK8),sK19(sK8,sK8))
| ~ r3(sK8,sK8,sK11(sK8,sK8)) ),
inference(instantiation,[status(thm)],[c_1836]) ).
tcf(c_1929,plain,
! [X0: $i] :
( id(sK3(X0),sK8)
| ~ r1(sK3(X0)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1930,plain,
( id(sK3(sK8),sK8)
| ~ r1(sK3(sK8)) ),
inference(instantiation,[status(thm)],[c_1929]) ).
tcf(c_2303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X1)
| ~ r1(X0)
| ~ r1(sK19(X2,X3))
| ~ r2(X1,sK12(X0,X1))
| ~ id(sK11(X0,X1),sK19(X2,X3))
| ~ r4(X0,sK12(X0,X1),sK11(X0,X1)) ),
inference(instantiation,[status(thm)],[c_551]) ).
tcf(c_2306,plain,
( ~ r1(sK8)
| ~ r1(sK19(sK8,sK8))
| ~ r2(sK8,sK12(sK8,sK8))
| ~ id(sK11(sK8,sK8),sK19(sK8,sK8))
| ~ r4(sK8,sK12(sK8,sK8),sK11(sK8,sK8)) ),
inference(instantiation,[status(thm)],[c_2303]) ).
tcf(c_2367,plain,
! [X0: $i] :
( r1(sK3(X0))
| ~ r1(sK5(X0)) ),
inference(superposition,[status(thm)],[c_1003,c_65]) ).
tcf(c_2380,plain,
! [X0: $i] : r1(sK3(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2367,c_61]) ).
tcf(c_2417,plain,
r1(sK3(sK8)),
inference(instantiation,[status(thm)],[c_2380]) ).
tcf(c_3687,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(sK19(X0,X1))
| ~ r1(X2)
| ~ r3(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_90,c_65]) ).
tcf(c_3709,plain,
( r1(sK19(sK8,sK8))
| ~ r1(sK8)
| ~ r3(sK8,sK8,sK8) ),
inference(instantiation,[status(thm)],[c_3687]) ).
tcf(c_7591,plain,
! [X0: $i,X1: $i,X2: $i] :
( id(sK13(X0,X1),X2)
| ~ id(sK14(X0,X1),X2)
| ~ id(sK13(X0,X1),sK14(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1379]) ).
tcf(c_7592,plain,
( id(sK13(sK8,sK8),sK8)
| ~ id(sK14(sK8,sK8),sK8)
| ~ id(sK13(sK8,sK8),sK14(sK8,sK8)) ),
inference(instantiation,[status(thm)],[c_7591]) ).
tcf(c_8227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( r3(X4,X5,sK11(X2,X3))
| ~ id(X5,X0)
| ~ id(X4,sK13(X0,X1))
| ~ id(sK11(X2,X3),sK10(X0,X1))
| ~ r3(sK13(X0,X1),X0,sK10(X0,X1)) ),
inference(instantiation,[status(thm)],[c_534]) ).
tcf(c_8228,plain,
( r3(sK8,sK8,sK11(sK8,sK8))
| ~ id(sK8,sK8)
| ~ id(sK8,sK13(sK8,sK8))
| ~ id(sK11(sK8,sK8),sK10(sK8,sK8))
| ~ r3(sK13(sK8,sK8),sK8,sK10(sK8,sK8)) ),
inference(instantiation,[status(thm)],[c_8227]) ).
tcf(c_8229,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8228,c_7592,c_3709,c_2417,c_2306,c_1930,c_1838,c_1527,c_1298,c_1191,c_626,c_527,c_515,c_466,c_120,c_111,c_110,c_107,c_104,c_103,c_102,c_101,c_98,c_96,c_95,c_94,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN086+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.34 % Computer : n001.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Thu Sep 24 06:05:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.38 Running first-order theorem proving
% 0.09/0.38 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.40 % Proving...
% 4.81/1.28 % SZS status Started for theBenchmark.p
% 4.81/1.28 % SZS status Theorem for theBenchmark.p
% 4.81/1.28
% 4.81/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.81/1.28
% 4.81/1.28 % ------ iProver source info
% 4.81/1.28
% 4.81/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.81/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.81/1.28 % git: non_committed_changes: false
% 4.81/1.28
% 4.81/1.28 % ------ Parsing...
% 4.81/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.81/1.28
% 4.81/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.81/1.28
% 4.81/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.81/1.28 % ------ Proving...
% 4.81/1.28 % ------ Problem Properties
% 4.81/1.28
% 4.81/1.28 %
% 4.81/1.28 % clauses 43
% 4.81/1.28 % conjectures 1
% 4.81/1.28 % EPR 16
% 4.81/1.28 % Horn 39
% 4.81/1.28 % unary 18
% 4.81/1.28 % binary 13
% 4.81/1.28 % lits 94
% 4.81/1.28 % lits eq 0
% 4.81/1.28 % fd_pure 0
% 4.81/1.28 % fd_pseudo 0
% 4.81/1.29 % fd_cond 0
% 4.81/1.29 % fd_pseudo_cond 0
% 4.81/1.29 % AC symbols 0
% 4.81/1.29
% 4.81/1.29 % ------ Schedule dynamic 5 is on
% 4.81/1.29
% 4.81/1.29 % ------ no equalities: superposition off
% 4.81/1.29
% 4.81/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.81/1.29
% 4.81/1.29
% 4.81/1.29 % ------
% 4.81/1.29 % Current options:
% 4.81/1.29 % ------
% 4.81/1.29
% 4.81/1.29
% 4.81/1.29 %
% 4.81/1.29
% 4.81/1.29 % ------ Proving...
% 4.81/1.29 %
% 4.81/1.29
% 4.81/1.29 % SZS status Theorem for theBenchmark.p
% 4.81/1.29
% 4.81/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.81/1.29
% 4.81/1.29
%------------------------------------------------------------------------------