%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU177+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 02:55:46 PM UTC 2026
% Result : Theorem 4.72s 1.43s
% Output : CNFRefutation 4.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 15 unt; 0 def)
% Number of atoms : 159 ( 28 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 190 ( 75 ~; 75 |; 26 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 96 !; 22 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f17,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f21,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f23,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f94,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f95,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f131,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f160,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f161,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f202,plain,
? [X0,X1,X2] :
( relation(X2)
& in(ordered_pair(X0,X1),X2)
& ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) ) ),
inference(ennf_transformation,[],[f95]) ).
fof(f203,plain,
? [X0,X1,X2] :
( relation(X2)
& in(ordered_pair(X0,X1),X2)
& ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) ) ),
inference(flattening,[],[f202]) ).
fof(f277,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(nnf_transformation,[],[f160]) ).
fof(f278,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X5,X7),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X2,X4),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(rectify,[],[f277]) ).
fof(f279,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK17(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK15(X0,X1),X1)
| in(ordered_pair(sK15(X0,X1),sK16(X0,X1)),X0) )
& ( ~ in(sK15(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK15(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X2,sK15(X0,X1)),skolemize(X4,sK16(X0,X1)),skolemize(X7,sK17(X0,X5))],[f278]) ).
fof(f287,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f161]) ).
fof(f288,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f287]) ).
fof(f289,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK24(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK22(X0,X1),X1)
| in(ordered_pair(sK23(X0,X1),sK22(X0,X1)),X0) )
& ( ~ in(sK22(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK22(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23,sK24]),skolemize(X2,sK22(X0,X1)),skolemize(X4,sK23(X0,X1)),skolemize(X7,sK24(X0,X5))],[f288]) ).
fof(f311,plain,
( relation(sK36)
& in(ordered_pair(sK34,sK35),sK36)
& ( ~ in(sK35,relation_rng(sK36))
| ~ in(sK34,relation_dom(sK36)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34,sK35,sK36]),skolemize(X0,sK34),skolemize(X1,sK35),skolemize(X2,sK36)],[f203]) ).
fof(f329,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f387,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f279]) ).
fof(f404,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f289]) ).
fof(f408,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f485,plain,
relation(sK36),
inference(cnf_transformation,[],[f311]) ).
fof(f486,plain,
in(ordered_pair(sK34,sK35),sK36),
inference(cnf_transformation,[],[f311]) ).
fof(f487,plain,
( ~ in(sK35,relation_rng(sK36))
| ~ in(sK34,relation_dom(sK36)) ),
inference(cnf_transformation,[],[f311]) ).
fof(f537,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f131]) ).
fof(f554,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f408,f537]) ).
fof(f572,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f387,f554]) ).
fof(f576,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(unordered_pair(unordered_pair(X6,X5),unordered_pair(X6,X6)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f404,f554]) ).
fof(f602,plain,
in(unordered_pair(unordered_pair(sK34,sK35),unordered_pair(sK34,sK34)),sK36),
inference(definition_unfolding,[],[f486,f554]) ).
fof(f652,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f572]) ).
fof(f660,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),unordered_pair(X6,X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f576]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f329]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f652]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f660]) ).
tcf(c_206,negated_conjecture,
( ~ in(sK35,relation_rng(sK36))
| ~ in(sK34,relation_dom(sK36)) ),
inference(cnf_transformation,[],[f487]) ).
tcf(c_207,negated_conjecture,
in(unordered_pair(unordered_pair(sK34,sK35),unordered_pair(sK34,sK34)),sK36),
inference(cnf_transformation,[],[f602]) ).
tcf(c_208,negated_conjecture,
relation(sK36),
inference(cnf_transformation,[],[f485]) ).
tcf(c_324,plain,
in(unordered_pair(unordered_pair(sK34,sK34),unordered_pair(sK34,sK35)),sK36),
inference(demodulation,[status(thm)],[c_207,c_51]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_51,c_127]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_51,c_110]) ).
tcf(c_555,plain,
( in(sK35,relation_rng(sK36))
| ~ relation(sK36) ),
inference(superposition,[status(thm)],[c_324,c_379]) ).
tcf(c_674,plain,
( in(sK34,relation_dom(sK36))
| ~ relation(sK36) ),
inference(superposition,[status(thm)],[c_324,c_393]) ).
tcf(c_682,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_674,c_555,c_206,c_208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU177+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 13:04:20 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.50 Running first-order theorem proving
% 0.18/0.50 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
% 0.25/0.51
% 0.25/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.51
% 0.25/0.52 % Detected problem language: tptp
% 0.25/0.53 % Proving...
% 4.72/1.43 % SZS status Started for theBenchmark.p
% 4.72/1.43 % SZS status Theorem for theBenchmark.p
% 4.72/1.43
% 4.72/1.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.72/1.43
% 4.72/1.43 % ------ iProver source info
% 4.72/1.43
% 4.72/1.43 % git: date: 2026-07-19 20:42:38 +0200
% 4.72/1.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.72/1.43 % git: non_committed_changes: false
% 4.72/1.43
% 4.72/1.43 % ------ Parsing...
% 4.72/1.43 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.72/1.43 % ------ Proving...
% 4.72/1.43 % ------ Problem Properties
% 4.72/1.43
% 4.72/1.43 %
% 4.72/1.43 % clauses 224
% 4.72/1.43 % conjectures 3
% 4.72/1.43 % EPR 32
% 4.72/1.43 % Horn 176
% 4.72/1.43 % unary 50
% 4.72/1.43 % binary 87
% 4.72/1.43 % lits 514
% 4.72/1.43 % lits eq 120
% 4.72/1.43 % fd_pure 0
% 4.72/1.43 % fd_pseudo 0
% 4.72/1.43 % fd_cond 10
% 4.72/1.43 % fd_pseudo_cond 46
% 4.72/1.43 % AC symbols 0
% 4.72/1.43
% 4.72/1.43 % ------ Input Options Time Limit: Unbounded
% 4.72/1.43
% 4.72/1.43
% 4.72/1.43 % ------
% 4.72/1.43 % Current options:
% 4.72/1.43 % ------
% 4.72/1.43
% 4.72/1.43
% 4.72/1.43 %
% 4.72/1.43
% 4.72/1.43 % ------ Proving...
% 4.72/1.43 %
% 4.72/1.43
% 4.72/1.43 % SZS status Theorem for theBenchmark.p
% 4.72/1.43
% 4.72/1.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.72/1.44
% 4.72/1.44
%------------------------------------------------------------------------------