%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU177+1 : 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 : n009.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 3.28s 1.31s
% Output : CNFRefutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 19 unt; 3 def)
% Number of atoms : 204 ( 30 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 214 ( 88 ~; 86 |; 26 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 106 !; 22 ?; 28 :)
% 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(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(f24,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(f25,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)],[f24]) ).
fof(f26,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(f27,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(f35,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,[],[f25]) ).
fof(f36,plain,
? [X0,X1,X2] :
( relation(X2)
& in(ordered_pair(X0,X1),X2)
& ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) ) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f38,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f43,plain,
( relation(sK6)
& in(ordered_pair(sK4,sK5),sK6)
& ( ~ in(sK5,relation_rng(sK6))
| ~ in(sK4,relation_dom(sK6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f36]) ).
fof(f44,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,[],[f37]) ).
fof(f45,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,[],[f44]) ).
fof(f46,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK9(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK7(X0,X1),X1)
| in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0) )
& ( ~ in(sK7(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f45]) ).
fof(f47,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,[],[f38]) ).
fof(f48,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,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK12(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK10(X0,X1),X1)
| in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0) )
& ( ~ in(sK10(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK10(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X2,sK10(X0,X1)),skolemize(X4,sK11(X0,X1)),skolemize(X7,sK12(X0,X5))],[f48]) ).
fof(f51,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f66,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f67,plain,
relation(sK6),
inference(cnf_transformation,[],[f43]) ).
fof(f68,plain,
in(ordered_pair(sK4,sK5),sK6),
inference(cnf_transformation,[],[f43]) ).
fof(f69,plain,
( ~ in(sK5,relation_rng(sK6))
| ~ in(sK4,relation_dom(sK6)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f71,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f75,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f79,plain,
in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK6),
inference(definition_unfolding,[],[f68,f66]) ).
fof(f82,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f71,f66]) ).
fof(f86,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f75,f66]) ).
fof(f88,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f82]) ).
fof(f90,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f86]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f51]) ).
tcf(c_65,negated_conjecture,
( ~ in(sK5,relation_rng(sK6))
| ~ in(sK4,relation_dom(sK6)) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_66,negated_conjecture,
in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK6),
inference(cnf_transformation,[],[f79]) ).
tcf(c_67,negated_conjecture,
relation(sK6),
inference(cnf_transformation,[],[f67]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_219,plain,
in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK5)),sK6),
inference(demodulation,[status(thm)],[c_66,c_50]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_74,c_50]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_70,c_50]) ).
tcf(c_480,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_dom(X0))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_246]) ).
tcf(c_481,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK6))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6) ),
inference(unflattening,[status(thm)],[c_480]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,relation_rng(X0))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_236]) ).
tcf(c_490,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(sK6))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6) ),
inference(unflattening,[status(thm)],[c_489]) ).
tcf(c_570,definition,
iPr_def_12 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_571,definition,
iPr_def_13 = unordered_pair(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_572,definition,
iPr_def_14 = unordered_pair(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_576,plain,
! [X0: $i,X1: $i] :
( in(X1,iPr_def_11)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6) ),
inference(demodulation,[status(thm)],[c_490]) ).
tcf(c_577,plain,
! [X0: $i,X1: $i] :
( in(X0,iPr_def_10)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6) ),
inference(demodulation,[status(thm)],[c_481]) ).
tcf(c_581,plain,
in(iPr_def_14,sK6),
inference(demodulation,[status(thm)],[c_219,c_571,c_570,c_572]) ).
tcf(c_582,negated_conjecture,
( ~ in(sK5,iPr_def_11)
| ~ in(sK4,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_1150,plain,
( in(sK4,iPr_def_10)
| ~ in(unordered_pair(singleton(sK4),iPr_def_13),sK6) ),
inference(superposition,[status(thm)],[c_571,c_577]) ).
tcf(c_1151,plain,
( in(sK5,iPr_def_11)
| ~ in(unordered_pair(singleton(sK4),iPr_def_13),sK6) ),
inference(superposition,[status(thm)],[c_571,c_576]) ).
tcf(c_1152,plain,
( in(sK5,iPr_def_11)
| ~ in(iPr_def_14,sK6) ),
inference(light_normalisation,[status(thm)],[c_1151,c_570,c_572]) ).
tcf(c_1153,plain,
in(sK5,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_1152,c_581]) ).
tcf(c_1154,plain,
( in(sK4,iPr_def_10)
| ~ in(iPr_def_14,sK6) ),
inference(light_normalisation,[status(thm)],[c_1150,c_570,c_572]) ).
tcf(c_1155,plain,
in(sK4,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1154,c_581]) ).
tcf(c_1162,plain,
~ in(sK4,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_582,c_1153]) ).
tcf(c_1163,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1162,c_1155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU177+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:03:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 3.28/1.31 % SZS status Started for theBenchmark.p
% 3.28/1.31 % SZS status Theorem for theBenchmark.p
% 3.28/1.31
% 3.28/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.28/1.31
% 3.28/1.31 % ------ iProver source info
% 3.28/1.31
% 3.28/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.28/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.28/1.31 % git: non_committed_changes: false
% 3.28/1.31
% 3.28/1.31 % ------ Parsing...
% 3.28/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.28/1.31
% 3.28/1.31 % ------ Preprocessing... sup_sim: 9 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 3.28/1.31
% 3.28/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.28/1.31
% 3.28/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.28/1.31 % ------ Proving...
% 3.28/1.31 % ------ Problem Properties
% 3.28/1.31
% 3.28/1.31 %
% 3.28/1.31 % clauses 35
% 3.28/1.31 % conjectures 1
% 3.28/1.31 % EPR 10
% 3.28/1.31 % Horn 30
% 3.28/1.31 % unary 13
% 3.28/1.31 % binary 13
% 3.28/1.31 % lits 66
% 3.28/1.31 % lits eq 16
% 3.28/1.31 % fd_pure 0
% 3.28/1.31 % fd_pseudo 0
% 3.28/1.31 % fd_cond 9
% 3.28/1.31 % fd_pseudo_cond 1
% 3.28/1.31 % AC symbols 0
% 3.28/1.31
% 3.28/1.31 % ------ Schedule dynamic 5 is on
% 3.28/1.31
% 3.28/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.28/1.31
% 3.28/1.31
% 3.28/1.31 % ------
% 3.28/1.31 % Current options:
% 3.28/1.31 % ------
% 3.28/1.31
% 3.28/1.31
% 3.28/1.31 %
% 3.28/1.31
% 3.28/1.31 % ------ Proving...
% 3.28/1.31 %
% 3.28/1.31
% 3.28/1.31 % SZS status Theorem for theBenchmark.p
% 3.28/1.31
% 3.28/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.28/1.31
% 3.28/1.31
%------------------------------------------------------------------------------