%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET996+1 : 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 : n020.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 02:49:17 PM UTC 2026
% Result : Theorem 114.02s 35.95s
% Output : CNFRefutation 114.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 141 ( 34 unt; 0 def)
% Number of atoms : 427 ( 97 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 502 ( 216 ~; 214 |; 51 &)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 289 ( 1 sgn 271 !; 18 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f6,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f10,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f13,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f14,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f23,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f24,axiom,
! [X0,X1,X2] :
( element(X2,X0)
=> ? [X3] :
( ! [X4] :
( in(X4,X1)
=> apply(X3,X4) = X2 )
& relation_dom(X3) = X1
& function(X3)
& relation(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e4_16_2__funct_1) ).
fof(f25,conjecture,
! [X0,X1] :
~ ( ! [X2] :
( ( function(X2)
& relation(X2) )
=> ~ ( subset(relation_rng(X2),X0)
& X1 = relation_dom(X2) ) )
& ~ ( X1 != empty_set
& X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1] :
~ ( ! [X2] :
( ( function(X2)
& relation(X2) )
=> ~ ( subset(relation_rng(X2),X0)
& X1 = relation_dom(X2) ) )
& ~ ( X1 != empty_set
& X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f28,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f29,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f30,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f33,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f36,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f23]) ).
fof(f40,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f43]) ).
fof(f49,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f50,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ? [X3] :
( ! [X4] :
( ~ in(X4,X1)
| apply(X3,X4) = X2 )
& relation_dom(X3) = X1
& function(X3)
& relation(X3) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f53,plain,
? [X0,X1] :
( ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ subset(relation_rng(X2),X0)
| relation_dom(X2) != X1 )
& ( empty_set = X1
| empty_set != X0 ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f54,plain,
? [X0,X1] :
( ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ subset(relation_rng(X2),X0)
| relation_dom(X2) != X1 )
& ( empty_set = X1
| empty_set != X0 ) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f56,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f57,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f56]) ).
fof(f61,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f33]) ).
fof(f64,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f65,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f65]) ).
fof(f67,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f68,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK3(X0,X5)) = X5
& in(sK3(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| ( sK1(X0,X1) = apply(X0,sK2(X0,X1))
& in(sK2(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK1(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK1(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f68]) ).
fof(f70,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f6]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ( ! [X4] :
( ~ in(X4,X1)
| apply(sK13(X1,X2),X4) = X2 )
& relation_dom(sK13(X1,X2)) = X1
& function(sK13(X1,X2))
& relation(sK13(X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X3,sK13(X1,X2))],[f52]) ).
fof(f80,plain,
( ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ subset(relation_rng(X2),sK14)
| relation_dom(X2) != sK15 )
& ( empty_set = sK15
| empty_set != sK14 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f54]) ).
fof(f81,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f83,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f85,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f86,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f87,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f88,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| apply(X0,sK3(X0,X5)) = X5 ),
inference(cnf_transformation,[],[f69]) ).
fof(f89,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(sK3(X0,X5),relation_dom(X0)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f90,plain,
! [X0,X1,X6,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| in(X5,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f94,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f70]) ).
fof(f99,plain,
relation(empty_set),
inference(cnf_transformation,[],[f10]) ).
fof(f100,plain,
empty(empty_set),
inference(cnf_transformation,[],[f10]) ).
fof(f104,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f106,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f120,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f36]) ).
fof(f121,plain,
! [X2,X0,X1,X4] :
( ~ element(X2,X0)
| ~ in(X4,X1)
| apply(sK13(X1,X2),X4) = X2 ),
inference(cnf_transformation,[],[f79]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| relation_dom(sK13(X1,X2)) = X1 ),
inference(cnf_transformation,[],[f79]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| function(sK13(X1,X2)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| relation(sK13(X1,X2)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f125,plain,
! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ subset(relation_rng(X2),sK14)
| relation_dom(X2) != sK15 ),
inference(cnf_transformation,[],[f80]) ).
fof(f126,plain,
( empty_set = sK15
| empty_set != sK14 ),
inference(cnf_transformation,[],[f80]) ).
fof(f127,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f128,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f129,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f29]) ).
fof(f131,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f134,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f61]) ).
fof(f137,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),X1) ),
inference(equality_resolution,[],[f90]) ).
fof(f138,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f137]) ).
fof(f139,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(sK3(X0,X5),relation_dom(X0)) ),
inference(equality_resolution,[],[f89]) ).
fof(f140,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| apply(X0,sK3(X0,X5)) = X5 ),
inference(equality_resolution,[],[f88]) ).
tcf(c_50,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( in(sK3(X1,X0),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK3(X1,X0)) = X0 )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_61,plain,
! [X0: $i] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f94]) ).
tcf(c_66,plain,
empty(empty_set),
inference(cnf_transformation,[],[f100]) ).
tcf(c_67,plain,
relation(empty_set),
inference(cnf_transformation,[],[f99]) ).
tcf(c_70,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_72,plain,
! [X0: $i] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_87,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f120]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(sK13(X2,X0))
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(sK13(X2,X0))
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK13(X2,X0)) = X2 )
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(sK13(X1,X2),X0) = X2 )
| ~ element(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_92,negated_conjecture,
( ( empty_set = sK15 )
| ( empty_set != sK14 ) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_93,negated_conjecture,
! [X0: $i] :
( ~ relation(X0)
| ~ function(X0)
| ~ subset(relation_rng(X0),sK14)
| ( relation_dom(X0) != sK15 ) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_96,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_101,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_6305,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(sK13(X2,X0))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_97,c_89]) ).
tcf(c_6326,plain,
! [X0: $i,X1: $i] : function(sK13(X0,X1)),
inference(superposition,[status(thm)],[c_87,c_6305]) ).
tcf(c_6700,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(sK13(X2,X0))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_97,c_88]) ).
tcf(c_6708,plain,
! [X0: $i,X1: $i] : relation(sK13(X0,X1)),
inference(superposition,[status(thm)],[c_87,c_6700]) ).
tcf(c_90494,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_66,c_50]) ).
tcf(c_90498,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_70,c_101]) ).
tcf(c_90501,plain,
! [X0: $i] :
( ( relation_rng(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_72,c_101]) ).
tcf(c_90526,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK13(X2,X0)) = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_97,c_90]) ).
tcf(c_90546,plain,
! [X0: $i,X1: $i] : relation_dom(sK13(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_87,c_90526]) ).
tcf(c_90554,plain,
! [X0: $i] :
( empty(X0)
| in(sK4(X0),X0) ),
inference(superposition,[status(thm)],[c_61,c_95]) ).
tcf(c_90565,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),X1)
| ( apply(X0,sK3(X0,sK0(relation_rng(X0),X1))) = sK0(relation_rng(X0),X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_53,c_60]) ).
tcf(c_90582,plain,
! [X0: $i,X1: $i] :
( ~ relation(sK13(X0,X1))
| ~ function(sK13(X0,X1))
| ~ subset(relation_rng(sK13(X0,X1)),sK14)
| ( X0 != sK15 ) ),
inference(superposition,[status(thm)],[c_90546,c_93]) ).
tcf(c_90584,plain,
! [X0: $i,X1: $i] :
( ~ subset(relation_rng(sK13(X0,X1)),sK14)
| ( X0 != sK15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90582,c_6708,c_6326]) ).
tcf(c_90594,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK0(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_90598,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X0),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ subset(relation_dom(X1),X2)
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_59,c_54]) ).
tcf(c_90614,plain,
! [X0: $i] : ~ subset(relation_rng(sK13(sK15,X0)),sK14),
inference(equality_resolution,[status(thm)],[c_90584]) ).
tcf(c_90617,plain,
! [X0: $i] :
( ( apply(sK13(sK15,X0),sK3(sK13(sK15,X0),sK0(relation_rng(sK13(sK15,X0)),sK14))) = sK0(relation_rng(sK13(sK15,X0)),sK14) )
| ~ relation(sK13(sK15,X0))
| ~ function(sK13(sK15,X0)) ),
inference(superposition,[status(thm)],[c_90565,c_90614]) ).
tcf(c_90618,plain,
! [X0: $i] : apply(sK13(sK15,X0),sK3(sK13(sK15,X0),sK0(relation_rng(sK13(sK15,X0)),sK14))) = sK0(relation_rng(sK13(sK15,X0)),sK14),
inference(forward_subsumption_resolution,[status(thm)],[c_90617,c_6708,c_6326]) ).
tcf(c_93877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X0,X4)
| ( apply(sK13(X1,X2),sK0(X0,X4)) = X2 )
| ~ element(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_90594,c_91]) ).
tcf(c_93892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(sK13(X2,X3),sK3(X1,X0)) = X3 )
| ~ relation(X1)
| ~ function(X1)
| ~ element(X3,X4)
| ~ subset(relation_dom(X1),X2)
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_90598,c_91]) ).
tcf(c_99744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X2,X4)
| ( apply(sK13(X3,X0),sK0(X2,X4)) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_97,c_93877]) ).
tcf(c_99835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| ( apply(sK13(X1,X2),sK0(X0,X3)) = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_87,c_99744]) ).
tcf(c_99845,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ( apply(sK13(X0,X1),sK0(X0,X2)) = X1 ) ),
inference(superposition,[status(thm)],[c_87,c_99835]) ).
tcf(c_99865,plain,
! [X0: $i,X1: $i] : apply(sK13(relation_rng(sK13(sK15,X0)),X1),sK0(relation_rng(sK13(sK15,X0)),sK14)) = X1,
inference(superposition,[status(thm)],[c_99845,c_90614]) ).
tcf(c_99961,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(sK13(relation_rng(sK13(sK15,X0)),X1)))
| ~ relation(sK13(relation_rng(sK13(sK15,X0)),X1))
| ~ function(sK13(relation_rng(sK13(sK15,X0)),X1))
| ~ in(sK0(relation_rng(sK13(sK15,X0)),sK14),relation_dom(sK13(relation_rng(sK13(sK15,X0)),X1))) ),
inference(superposition,[status(thm)],[c_99865,c_58]) ).
tcf(c_99962,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(sK13(relation_rng(sK13(sK15,X0)),X1)))
| ~ relation(sK13(relation_rng(sK13(sK15,X0)),X1))
| ~ function(sK13(relation_rng(sK13(sK15,X0)),X1))
| ~ in(sK0(relation_rng(sK13(sK15,X0)),sK14),relation_rng(sK13(sK15,X0))) ),
inference(demodulation,[status(thm)],[c_99961,c_90546]) ).
tcf(c_99963,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(sK13(relation_rng(sK13(sK15,X0)),X1)))
| ~ in(sK0(relation_rng(sK13(sK15,X0)),sK14),relation_rng(sK13(sK15,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_99962,c_6708,c_6326]) ).
tcf(c_99968,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(sK13(sK15,X1)),sK14)
| in(X0,relation_rng(sK13(relation_rng(sK13(sK15,X1)),X0))) ),
inference(superposition,[status(thm)],[c_53,c_99963]) ).
tcf(c_99972,plain,
! [X0: $i,X1: $i] : in(X0,relation_rng(sK13(relation_rng(sK13(sK15,X1)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_99968,c_90614]) ).
tcf(c_99977,plain,
! [X0: $i,X1: $i] : element(X0,relation_rng(sK13(relation_rng(sK13(sK15,X1)),X0))),
inference(superposition,[status(thm)],[c_99972,c_94]) ).
tcf(c_113942,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_66,c_90498]) ).
tcf(c_114477,plain,
( ~ relation(empty_set)
| ~ function(empty_set)
| ~ subset(relation_rng(empty_set),sK14)
| ( empty_set != sK15 ) ),
inference(superposition,[status(thm)],[c_113942,c_93]) ).
tcf(c_114480,plain,
( ~ subset(relation_rng(empty_set),sK14)
| ( empty_set != sK15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_114477,c_67,c_90494]) ).
tcf(c_114588,plain,
relation_rng(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_66,c_90501]) ).
tcf(c_114885,plain,
( ~ subset(empty_set,sK14)
| ( empty_set != sK15 ) ),
inference(light_normalisation,[status(thm)],[c_114480,c_114588]) ).
tcf(c_114886,plain,
empty_set != sK15,
inference(forward_subsumption_resolution,[status(thm)],[c_114885,c_96]) ).
tcf(c_114891,plain,
empty_set != sK14,
inference(backward_subsumption_resolution,[status(thm)],[c_92,c_114886]) ).
tcf(c_129582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(relation_rng(X0),X4)
| ( apply(sK13(X1,X2),sK3(X0,sK0(relation_rng(X0),X4))) = X2 )
| ~ relation(X0)
| ~ function(X0)
| ~ element(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_53,c_93892]) ).
tcf(c_129981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_rng(X2),X3)
| ( apply(sK13(relation_dom(X2),X0),sK3(X2,sK0(relation_rng(X2),X3))) = X0 )
| ~ relation(X2)
| ~ function(X2)
| ~ element(X0,X1) ),
inference(superposition,[status(thm)],[c_87,c_129582]) ).
tcf(c_130051,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(X0),X2)
| ( apply(sK13(relation_dom(X0),X1),sK3(X0,sK0(relation_rng(X0),X2))) = X1 )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_99977,c_129981]) ).
tcf(c_131922,plain,
! [X0: $i,X1: $i] :
( ( apply(sK13(relation_dom(sK13(sK15,X0)),X1),sK3(sK13(sK15,X0),sK0(relation_rng(sK13(sK15,X0)),sK14))) = X1 )
| ~ relation(sK13(sK15,X0))
| ~ function(sK13(sK15,X0)) ),
inference(superposition,[status(thm)],[c_130051,c_90614]) ).
tcf(c_131970,plain,
! [X0: $i,X1: $i] :
( ( apply(sK13(sK15,X1),sK3(sK13(sK15,X0),sK0(relation_rng(sK13(sK15,X0)),sK14))) = X1 )
| ~ relation(sK13(sK15,X0))
| ~ function(sK13(sK15,X0)) ),
inference(demodulation,[status(thm)],[c_131922,c_90546]) ).
tcf(c_131971,plain,
! [X0: $i,X1: $i] : apply(sK13(sK15,X0),sK3(sK13(sK15,X1),sK0(relation_rng(sK13(sK15,X1)),sK14))) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_131970,c_6708,c_6326]) ).
tcf(c_132062,plain,
! [X0: $i] : sK0(relation_rng(sK13(sK15,X0)),sK14) = X0,
inference(demodulation,[status(thm)],[c_90618,c_131971]) ).
tcf(c_132808,plain,
! [X0: $i] :
( subset(relation_rng(sK13(sK15,X0)),sK14)
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_132062,c_52]) ).
tcf(c_132814,plain,
! [X0: $i] : ~ in(X0,sK14),
inference(forward_subsumption_resolution,[status(thm)],[c_132808,c_90614]) ).
tcf(c_132832,plain,
empty(sK14),
inference(superposition,[status(thm)],[c_90554,c_132814]) ).
tcf(c_136056,plain,
empty_set = sK14,
inference(superposition,[status(thm)],[c_132832,c_101]) ).
tcf(c_136057,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_136056,c_114891]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET996+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:33:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 114.02/35.95 % SZS status Started for theBenchmark.p
% 114.02/35.95 % SZS status Theorem for theBenchmark.p
% 114.02/35.95
% 114.02/35.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 114.02/35.95
% 114.02/35.95 % ------ iProver source info
% 114.02/35.95
% 114.02/35.95 % git: date: 2026-07-19 20:42:38 +0200
% 114.02/35.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 114.02/35.95 % git: non_committed_changes: false
% 114.02/35.95
% 114.02/35.95 % ------ Parsing...
% 114.02/35.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 114.02/35.95
% 114.02/35.95 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 114.02/35.95
% 114.02/35.95 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 114.02/35.95
% 114.02/35.95 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 114.02/35.95 % ------ Proving...
% 114.02/35.95 % ------ Problem Properties
% 114.02/35.95
% 114.02/35.95 %
% 114.02/35.95 % clauses 52
% 114.02/35.95 % conjectures 2
% 114.02/35.95 % EPR 25
% 114.02/35.95 % Horn 47
% 114.02/35.95 % unary 17
% 114.02/35.95 % binary 20
% 114.02/35.95 % lits 113
% 114.02/35.95 % lits eq 13
% 114.02/35.95 % fd_pure 0
% 114.02/35.95 % fd_pseudo 0
% 114.02/35.95 % fd_cond 1
% 114.02/35.95 % fd_pseudo_cond 4
% 114.02/35.95 % AC symbols 0
% 114.02/35.95
% 114.02/35.95 % ------ Input Options Time Limit: Unbounded
% 114.02/35.95
% 114.02/35.95
% 114.02/35.95 % ------
% 114.02/35.95 % Current options:
% 114.02/35.95 % ------
% 114.02/35.95
% 114.02/35.95
% 114.02/35.95 %
% 114.02/35.95
% 114.02/35.95 % ------ Proving...
% 114.02/35.95 %
% 114.02/35.95
% 114.02/35.95 % SZS status Theorem for theBenchmark.p
% 114.02/35.95
% 114.02/35.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 114.02/35.96
% 114.02/35.96
%------------------------------------------------------------------------------