%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU211+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 : n007.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 02:55:55 PM UTC 2026
% Result : Theorem 6.07s 11.77s
% Output : CNFRefutation 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 13 unt; 0 def)
% Number of atoms : 188 ( 18 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 231 ( 96 ~; 94 |; 29 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 149 ( 0 sgn 133 !; 16 ?; 39 :)
% 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(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6,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(f28,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f41,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f44,plain,
? [X0,X1,X2] :
( relation(X2)
& subset(X0,X1)
& ~ subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f45,plain,
? [X0,X1,X2] :
( relation(X2)
& subset(X0,X1)
& ~ subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(flattening,[],[f44]) ).
fof(f55,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f56,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(X6,sK2(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK0(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f56]) ).
fof(f58,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(f59,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,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK3(X0,X1),X0)
& ~ in(sK3(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f59]) ).
fof(f68,plain,
( relation(sK13)
& subset(sK11,sK12)
& ~ subset(relation_inverse_image(sK13,sK11),relation_inverse_image(sK13,sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f45]) ).
fof(f72,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f73,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK2(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f74,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(X6,sK2(X0,X1,X6)),X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f75,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f79,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f80,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f81,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f102,plain,
relation(sK13),
inference(cnf_transformation,[],[f68]) ).
fof(f103,plain,
subset(sK11,sK12),
inference(cnf_transformation,[],[f68]) ).
fof(f104,plain,
~ subset(relation_inverse_image(sK13,sK11),relation_inverse_image(sK13,sK12)),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f75,f82]) ).
fof(f117,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(X6,sK2(X0,X1,X6)),singleton(X6)),X0) ),
inference(definition_unfolding,[],[f74,f82]) ).
fof(f119,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f116]) ).
fof(f120,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(unordered_pair(unordered_pair(X6,sK2(X0,X1,X6)),singleton(X6)),X0) ),
inference(equality_resolution,[],[f117]) ).
fof(f121,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(sK2(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f73]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f72]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK2(X1,X2,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_80,negated_conjecture,
~ subset(relation_inverse_image(sK13,sK11),relation_inverse_image(sK13,sK12)),
inference(cnf_transformation,[],[f104]) ).
tcf(c_81,negated_conjecture,
subset(sK11,sK12),
inference(cnf_transformation,[],[f103]) ).
tcf(c_82,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f102]) ).
tcf(c_372,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_56,c_51]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_55,c_51]) ).
tcf(c_3688,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ in(X0,sK11) ),
inference(resolution,[status(thm)],[c_60,c_81]) ).
tcf(c_4225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,relation_inverse_image(X0,X3))
| ~ relation(X0)
| ~ in(X2,relation_inverse_image(X0,X1))
| ~ in(sK2(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[c_373,c_372]) ).
tcf(c_4434,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,relation_inverse_image(X0,sK12))
| ~ relation(X0)
| ~ in(X2,relation_inverse_image(X0,X1))
| ~ in(sK2(X0,X1,X2),sK11) ),
inference(resolution,[status(thm)],[c_4225,c_3688]) ).
tcf(c_4478,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_inverse_image(X1,sK12))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,sK11)) ),
inference(resolution,[status(thm)],[c_4434,c_57]) ).
tcf(c_4497,plain,
! [X0: $i,X1: $i] :
( subset(X0,relation_inverse_image(X1,sK12))
| ~ relation(X1)
| ~ in(sK3(X0,relation_inverse_image(X1,sK12)),relation_inverse_image(X1,sK11)) ),
inference(resolution,[status(thm)],[c_4478,c_58]) ).
tcf(c_4563,plain,
! [X0: $i] :
( subset(relation_inverse_image(X0,sK11),relation_inverse_image(X0,sK12))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[c_4497,c_59]) ).
tcf(c_5040,plain,
~ relation(sK13),
inference(resolution,[status(thm)],[c_4563,c_80]) ).
tcf(c_5041,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5040,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU211+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.37 % Computer : n007.cluster.edu
% 0.11/10.37 % Model : x86_64 x86_64
% 0.11/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.37 % Memory : 8046.5625MB
% 0.11/10.37 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Thu Sep 24 13:09:48 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/10.42 Running first-order theorem proving
% 0.16/10.42 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
% 0.16/10.43
% 0.16/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.43
% 0.16/10.43 % Detected problem language: tptp
% 0.16/10.45 % Proving...
% 6.07/11.77 % SZS status Started for theBenchmark.p
% 6.07/11.77 % SZS status Theorem for theBenchmark.p
% 6.07/11.77
% 6.07/11.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.07/11.77
% 6.07/11.77 % ------ iProver source info
% 6.07/11.77
% 6.07/11.77 % git: date: 2026-07-19 20:42:38 +0200
% 6.07/11.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.07/11.77 % git: non_committed_changes: false
% 6.07/11.77
% 6.07/11.77 % ------ Parsing...
% 6.07/11.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.07/11.77
% 6.07/11.77 % ------ Preprocessing... sup_sim: 4 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 %
% 6.07/11.77
% 6.07/11.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.07/11.77
% 6.07/11.77 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.07/11.77 % ------ Proving...
% 6.07/11.77 % ------ Problem Properties
% 6.07/11.77
% 6.07/11.77 %
% 6.07/11.77 % clauses 41
% 6.07/11.77 % conjectures 3
% 6.07/11.77 % EPR 21
% 6.07/11.77 % Horn 36
% 6.07/11.77 % unary 19
% 6.07/11.77 % binary 11
% 6.07/11.77 % lits 79
% 6.07/11.77 % lits eq 6
% 6.07/11.77 % fd_pure 0
% 6.07/11.77 % fd_pseudo 0
% 6.07/11.77 % fd_cond 1
% 6.07/11.77 % fd_pseudo_cond 4
% 6.07/11.77 % AC symbols 0
% 6.07/11.77
% 6.07/11.77 % ------ Input Options Time Limit: Unbounded
% 6.07/11.77
% 6.07/11.77
% 6.07/11.77 % ------
% 6.07/11.77 % Current options:
% 6.07/11.77 % ------
% 6.07/11.77
% 6.07/11.77
% 6.07/11.77 %
% 6.07/11.77
% 6.07/11.77 % ------ Proving...
% 6.07/11.77 %
% 6.07/11.77
% 6.07/11.77 % SZS status Theorem for theBenchmark.p
% 6.07/11.77
% 6.07/11.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.07/11.77
% 6.07/11.77
%------------------------------------------------------------------------------