%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n010.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 02:55:37 PM UTC 2026
% Result : Theorem 0.44s 1.28s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 14 unt; 2 def)
% Number of atoms : 115 ( 79 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 129 ( 52 ~; 47 |; 28 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 57 ( 0 sgn 50 !; 7 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,conjecture,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f9,plain,
? [X0,X1,X2,X3] :
( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| sK0(X0,X1,X2) = X1
| sK0(X0,X1,X2) = X0 )
& ( ~ in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) != X1
& sK0(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f12]) ).
fof(f16,plain,
( sK3 != sK6
& sK3 != sK5
& unordered_pair(sK3,sK4) = unordered_pair(sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f9]) ).
fof(f19,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| ~ in(X4,X2)
| X1 = X4
| X0 = X4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
sK3 != sK6,
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
sK3 != sK5,
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
unordered_pair(sK3,sK4) = unordered_pair(sK5,sK6),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f21]) ).
fof(f31,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f30]) ).
fof(f34,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f19]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_59,negated_conjecture,
unordered_pair(sK3,sK4) = unordered_pair(sK5,sK6),
inference(cnf_transformation,[],[f29]) ).
tcf(c_60,negated_conjecture,
sK3 != sK5,
inference(cnf_transformation,[],[f28]) ).
tcf(c_61,negated_conjecture,
sK3 != sK6,
inference(cnf_transformation,[],[f27]) ).
tcf(c_230,definition,
iPr_def_10 = unordered_pair(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_231,definition,
iPr_def_11 = unordered_pair(sK5,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_234,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_59,c_231,c_230]) ).
tcf(c_385,plain,
in(sK3,iPr_def_10),
inference(superposition,[status(thm)],[c_230,c_54]) ).
tcf(c_386,plain,
unordered_pair(sK5,sK6) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_231,c_234]) ).
tcf(c_410,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ( X0 = sK5 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_386,c_56]) ).
tcf(c_417,plain,
( ( sK3 = sK6 )
| ( sK3 = sK5 )
| ~ in(sK3,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_410]) ).
tcf(c_418,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_417,c_385,c_60,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.36 % Computer : n010.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8046.5625MB
% 0.13/0.36 % OS : Linux 6.8.0-71-generic
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Sep 24 12:58:15 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 0.44/1.28 % SZS status Started for theBenchmark.p
% 0.44/1.28 % SZS status Theorem for theBenchmark.p
% 0.44/1.28
% 0.44/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.44/1.28
% 0.44/1.28 % ------ iProver source info
% 0.44/1.28
% 0.44/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.44/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.44/1.28 % git: non_committed_changes: false
% 0.44/1.28
% 0.44/1.28 % ------ Parsing...
% 0.44/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.44/1.28
% 0.44/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 0.44/1.28
% 0.44/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.44/1.28
% 0.44/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.44/1.28 % ------ Proving...
% 0.44/1.28 % ------ Problem Properties
% 0.44/1.28
% 0.44/1.28 %
% 0.44/1.28 % clauses 14
% 0.44/1.28 % conjectures 3
% 0.44/1.28 % EPR 5
% 0.44/1.28 % Horn 12
% 0.44/1.28 % unary 9
% 0.44/1.28 % binary 1
% 0.44/1.28 % lits 24
% 0.44/1.28 % lits eq 16
% 0.44/1.28 % fd_pure 0
% 0.44/1.28 % fd_pseudo 0
% 0.44/1.28 % fd_cond 0
% 0.44/1.28 % fd_pseudo_cond 3
% 0.44/1.28 % AC symbols 0
% 0.44/1.28
% 0.44/1.28 % ------ Schedule dynamic 5 is on
% 0.44/1.28
% 0.44/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.44/1.28
% 0.44/1.28
% 0.44/1.28 % ------
% 0.44/1.28 % Current options:
% 0.44/1.28 % ------
% 0.44/1.28
% 0.44/1.28
% 0.44/1.28 %
% 0.44/1.28
% 0.44/1.28 % ------ Proving...
% 0.44/1.28 %
% 0.44/1.28
% 0.44/1.28 % SZS status Theorem for theBenchmark.p
% 0.44/1.28
% 0.44/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.44/1.28
% 0.44/1.28
%------------------------------------------------------------------------------