%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU156+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 : n006.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 02:55:39 PM UTC 2026
% Result : Theorem 3.29s 1.19s
% Output : CNFRefutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 86 ( 31 unt; 6 def)
% Number of atoms : 229 ( 152 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 137 ( 61 ~; 65 |; 6 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 119 ( 1 sgn 115 !; 4 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f2,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(f6,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f7,axiom,
! [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(f8,conjecture,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f11,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f12,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f14,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f6]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f7]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
& ( X1 != X3
| X0 != X2 ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0,X1,X2] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1,X2] :
( singleton(X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(ennf_transformation,[],[f13]) ).
fof(f22,plain,
( ordered_pair(sK2,sK3) = ordered_pair(sK4,sK5)
& ( sK3 != sK5
| sK2 != sK4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f16]) ).
fof(f23,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
ordered_pair(sK2,sK3) = ordered_pair(sK4,sK5),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
( sK3 != sK5
| sK2 != sK4 ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f24,f32]) ).
fof(f38,plain,
unordered_pair(unordered_pair(sK2,sK3),unordered_pair(sK2,sK2)) = unordered_pair(unordered_pair(sK4,sK5),unordered_pair(sK4,sK4)),
inference(definition_unfolding,[],[f30,f36,f36]) ).
fof(f39,plain,
! [X0,X1] :
( ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1))
| X0 = X1 ),
inference(definition_unfolding,[],[f33,f32,f32]) ).
fof(f40,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(definition_unfolding,[],[f34,f32]) ).
fof(f41,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(definition_unfolding,[],[f35,f32]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f23]) ).
tcf(c_53,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( X0 = X2 )
| ( unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_55,negated_conjecture,
( ( sK3 != sK5 )
| ( sK2 != sK4 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_56,negated_conjecture,
unordered_pair(unordered_pair(sK2,sK3),unordered_pair(sK2,sK2)) = unordered_pair(unordered_pair(sK4,sK5),unordered_pair(sK4,sK4)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_113,plain,
unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK3)) = unordered_pair(unordered_pair(sK4,sK4),unordered_pair(sK4,sK5)),
inference(demodulation,[status(thm)],[c_56,c_49]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(X2,X2) != X1 )
| ( unordered_pair(X0,X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_57]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X1) ) ),
inference(unflattening,[status(thm)],[c_137]) ).
tcf(c_214,definition,
iPr_def_10 = unordered_pair(sK2,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_215,definition,
iPr_def_11 = unordered_pair(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_216,definition,
iPr_def_12 = unordered_pair(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_217,definition,
iPr_def_13 = unordered_pair(sK4,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_218,definition,
iPr_def_14 = unordered_pair(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_219,definition,
iPr_def_15 = unordered_pair(iPr_def_13,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_220,plain,
iPr_def_12 = iPr_def_15,
inference(demodulation,[status(thm)],[c_113,c_218,c_217,c_219,c_215,c_214,c_216]) ).
tcf(c_221,negated_conjecture,
( ( sK3 != sK5 )
| ( sK2 != sK4 ) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(X0,X2) = unordered_pair(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_367,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ( unordered_pair(X0,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_214,c_138]) ).
tcf(c_375,plain,
unordered_pair(iPr_def_13,iPr_def_14) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_219,c_220]) ).
tcf(c_434,plain,
( ( sK2 = sK4 )
| ( iPr_def_10 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_217,c_367]) ).
tcf(c_441,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK2 )
| ( unordered_pair(X0,X1) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_214,c_58]) ).
tcf(c_480,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( unordered_pair(X0,X1) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_214,c_59]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( X1 = X2 )
| ( unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_49,c_54]) ).
tcf(c_541,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_14 )
| ( X0 = iPr_def_13 )
| ( unordered_pair(X0,X1) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_375,c_54]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_14 )
| ( X1 = iPr_def_13 )
| ( unordered_pair(X0,X1) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_49,c_541]) ).
tcf(c_662,plain,
( ( iPr_def_10 = iPr_def_14 )
| ( iPr_def_10 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_216,c_541]) ).
tcf(c_713,plain,
! [X0: $i] :
( ( sK3 = sK5 )
| ( unordered_pair(X0,X0) != unordered_pair(sK3,sK5) ) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_714,plain,
( ( sK3 = sK5 )
| ( unordered_pair(sK2,sK2) != unordered_pair(sK3,sK5) ) ),
inference(instantiation,[status(thm)],[c_713]) ).
tcf(c_891,plain,
( ( sK2 = sK4 )
| ( iPr_def_10 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_218,c_441]) ).
tcf(c_906,plain,
sK2 = sK4,
inference(global_subsumption_just,[status(thm)],[c_891,c_434,c_662,c_891]) ).
tcf(c_913,plain,
unordered_pair(sK2,sK5) = iPr_def_14,
inference(demodulation,[status(thm)],[c_218,c_906]) ).
tcf(c_914,plain,
unordered_pair(sK2,sK2) = iPr_def_13,
inference(demodulation,[status(thm)],[c_217,c_906]) ).
tcf(c_915,plain,
( ( sK3 != sK5 )
| ( sK2 != sK2 ) ),
inference(demodulation,[status(thm)],[c_221,c_906]) ).
tcf(c_916,plain,
iPr_def_10 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_914,c_214]) ).
tcf(c_919,plain,
sK3 != sK5,
inference(equality_resolution_simp,[status(thm)],[c_915]) ).
tcf(c_932,plain,
unordered_pair(iPr_def_10,iPr_def_14) = iPr_def_12,
inference(demodulation,[status(thm)],[c_375,c_916]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_14 )
| ( X1 = iPr_def_10 )
| ( unordered_pair(X0,X1) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_656,c_916]) ).
tcf(c_1032,plain,
( ( iPr_def_11 = iPr_def_14 )
| ( iPr_def_10 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_216,c_1018]) ).
tcf(c_1147,plain,
( ( sK2 = sK3 )
| ( iPr_def_10 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_215,c_480]) ).
tcf(c_1150,plain,
( ( sK2 = sK5 )
| ( iPr_def_10 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_913,c_480]) ).
tcf(c_1334,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK3 )
| ( X0 = sK3 )
| ( unordered_pair(X0,X1) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_215,c_526]) ).
tcf(c_1338,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_14 )
| ( X0 = iPr_def_14 )
| ( unordered_pair(X0,X1) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_932,c_526]) ).
tcf(c_1341,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK3 )
| ( X1 = sK2 )
| ( unordered_pair(X0,X1) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_215,c_526]) ).
tcf(c_1467,plain,
( ( iPr_def_11 = iPr_def_14 )
| ( iPr_def_10 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_216,c_1338]) ).
tcf(c_1567,plain,
( ( sK3 = sK5 )
| ( sK2 = sK3 )
| ( iPr_def_11 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_913,c_1334]) ).
tcf(c_1569,plain,
( ( sK2 = sK3 )
| ( iPr_def_11 != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1567,c_919]) ).
tcf(c_1614,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = unordered_pair(sK3,sK5) )
| ( X0 != sK5 )
| ( X0 != sK3 ) ),
inference(instantiation,[status(thm)],[c_225]) ).
tcf(c_1615,plain,
( ( unordered_pair(sK2,sK2) = unordered_pair(sK3,sK5) )
| ( sK2 != sK5 )
| ( sK2 != sK3 ) ),
inference(instantiation,[status(thm)],[c_1614]) ).
tcf(c_1629,plain,
( ( sK3 = sK5 )
| ( sK2 = sK5 )
| ( iPr_def_11 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_913,c_1341]) ).
tcf(c_1631,plain,
( ( sK2 = sK5 )
| ( iPr_def_11 != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1629,c_919]) ).
tcf(c_1636,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1631,c_1615,c_1569,c_1467,c_1147,c_1150,c_1032,c_906,c_714,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU156+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 12:58:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 0.14/0.43 % Proving...
% 3.29/1.19 % SZS status Started for theBenchmark.p
% 3.29/1.19 % SZS status Theorem for theBenchmark.p
% 3.29/1.19
% 3.29/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.29/1.19
% 3.29/1.19 % ------ iProver source info
% 3.29/1.19
% 3.29/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.29/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.29/1.19 % git: non_committed_changes: false
% 3.29/1.19
% 3.29/1.19 % ------ Parsing...
% 3.29/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.29/1.19
% 3.29/1.19 % ------ Preprocessing... sup_sim: 1 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 %
% 3.29/1.19
% 3.29/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.29/1.19
% 3.29/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.29/1.19 % ------ Proving...
% 3.29/1.19 % ------ Problem Properties
% 3.29/1.19
% 3.29/1.19 %
% 3.29/1.19 % clauses 16
% 3.29/1.19 % conjectures 1
% 3.29/1.19 % EPR 4
% 3.29/1.19 % Horn 15
% 3.29/1.19 % unary 11
% 3.29/1.19 % binary 4
% 3.29/1.19 % lits 22
% 3.29/1.19 % lits eq 19
% 3.29/1.19 % fd_pure 0
% 3.29/1.19 % fd_pseudo 0
% 3.29/1.19 % fd_cond 0
% 3.29/1.19 % fd_pseudo_cond 4
% 3.29/1.19 % AC symbols 0
% 3.29/1.19
% 3.29/1.19 % ------ Schedule dynamic 5 is on
% 3.29/1.19
% 3.29/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.29/1.19
% 3.29/1.19
% 3.29/1.19 % ------
% 3.29/1.19 % Current options:
% 3.29/1.19 % ------
% 3.29/1.19
% 3.29/1.19
% 3.29/1.19 %
% 3.29/1.19
% 3.29/1.19 % ------ Proving...
% 3.29/1.19 %
% 3.29/1.19
% 3.29/1.19 % SZS status Theorem for theBenchmark.p
% 3.29/1.19
% 3.29/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.29/1.19
% 3.29/1.19
%------------------------------------------------------------------------------