%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 02:49:11 PM UTC 2026
% Result : Theorem 2.08s 1.28s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 26 unt; 7 def)
% Number of atoms : 148 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 94 ( 46 ~; 38 |; 7 &)
% ( 1 <=>; 2 =>; 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 : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 90 !; 4 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
=> in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
=> in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f11,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
& ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f12]) ).
fof(f16,plain,
( in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5))
& ~ in(ordered_pair(sK3,sK2),cartesian_product2(sK5,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f11]) ).
fof(f18,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f19,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
~ in(ordered_pair(sK3,sK2),cartesian_product2(sK5,sK4)),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f23,f19]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f22,f19]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f21,f19]) ).
fof(f32,plain,
~ in(unordered_pair(unordered_pair(sK3,sK2),singleton(sK3)),cartesian_product2(sK5,sK4)),
inference(definition_unfolding,[],[f27,f19]) ).
fof(f33,plain,
in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)),
inference(definition_unfolding,[],[f26,f19]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,negated_conjecture,
~ in(unordered_pair(unordered_pair(sK3,sK2),singleton(sK3)),cartesian_product2(sK5,sK4)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_58,negated_conjecture,
in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_96,plain,
in(unordered_pair(singleton(sK2),unordered_pair(sK3,sK2)),cartesian_product2(sK4,sK5)),
inference(demodulation,[status(thm)],[c_58,c_50]) ).
tcf(c_97,plain,
~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK2)),cartesian_product2(sK5,sK4)),
inference(demodulation,[status(thm)],[c_57,c_50]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(demodulation,[status(thm)],[c_54,c_50]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(demodulation,[status(thm)],[c_53,c_50]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_52,c_50]) ).
tcf(c_143,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_144,definition,
iPr_def_11 = unordered_pair(sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_145,definition,
iPr_def_12 = unordered_pair(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_146,definition,
iPr_def_13 = cartesian_product2(sK5,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_147,definition,
iPr_def_14 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_148,definition,
iPr_def_15 = unordered_pair(iPr_def_14,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_149,definition,
iPr_def_16 = cartesian_product2(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_150,plain,
~ in(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_97,c_146,c_144,c_143,c_145]) ).
tcf(c_151,plain,
in(iPr_def_15,iPr_def_16),
inference(demodulation,[status(thm)],[c_96,c_149,c_147,c_148]) ).
tcf(c_353,plain,
unordered_pair(iPr_def_11,iPr_def_14) = iPr_def_15,
inference(demodulation,[status(thm)],[c_148,c_50]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_16) ),
inference(superposition,[status(thm)],[c_149,c_98]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i] :
( in(X0,sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_16) ),
inference(superposition,[status(thm)],[c_149,c_105]) ).
tcf(c_455,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK3),iPr_def_11),cartesian_product2(X0,X1))
| ~ in(sK2,X1)
| ~ in(sK3,X0) ),
inference(superposition,[status(thm)],[c_144,c_112]) ).
tcf(c_475,plain,
! [X0: $i,X1: $i] :
( in(iPr_def_12,cartesian_product2(X0,X1))
| ~ in(sK2,X1)
| ~ in(sK3,X0) ),
inference(light_normalisation,[status(thm)],[c_455,c_143,c_145]) ).
tcf(c_700,plain,
! [X0: $i] :
( in(X0,sK5)
| ~ in(unordered_pair(iPr_def_14,unordered_pair(sK2,X0)),iPr_def_16) ),
inference(superposition,[status(thm)],[c_147,c_358]) ).
tcf(c_729,plain,
! [X0: $i] :
( in(X0,sK5)
| ~ in(unordered_pair(iPr_def_14,unordered_pair(X0,sK2)),iPr_def_16) ),
inference(superposition,[status(thm)],[c_50,c_700]) ).
tcf(c_739,plain,
( in(sK3,sK5)
| ~ in(unordered_pair(iPr_def_14,iPr_def_11),iPr_def_16) ),
inference(superposition,[status(thm)],[c_144,c_729]) ).
tcf(c_757,plain,
( in(sK3,sK5)
| ~ in(iPr_def_15,iPr_def_16) ),
inference(demodulation,[status(thm)],[c_739,c_50,c_353]) ).
tcf(c_758,plain,
in(sK3,sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_757,c_151]) ).
tcf(c_878,plain,
! [X0: $i] :
( in(sK2,sK4)
| ~ in(unordered_pair(iPr_def_14,unordered_pair(sK2,X0)),iPr_def_16) ),
inference(superposition,[status(thm)],[c_147,c_416]) ).
tcf(c_917,plain,
! [X0: $i] :
( in(sK2,sK4)
| ~ in(unordered_pair(iPr_def_14,unordered_pair(X0,sK2)),iPr_def_16) ),
inference(superposition,[status(thm)],[c_50,c_878]) ).
tcf(c_933,plain,
( in(sK2,sK4)
| ~ in(unordered_pair(iPr_def_14,iPr_def_11),iPr_def_16) ),
inference(superposition,[status(thm)],[c_144,c_917]) ).
tcf(c_973,plain,
( in(sK2,sK4)
| ~ in(iPr_def_15,iPr_def_16) ),
inference(demodulation,[status(thm)],[c_933,c_50,c_353]) ).
tcf(c_974,plain,
in(sK2,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_973,c_151]) ).
tcf(c_1166,plain,
( in(iPr_def_12,iPr_def_13)
| ~ in(sK2,sK4)
| ~ in(sK3,sK5) ),
inference(superposition,[status(thm)],[c_146,c_475]) ).
tcf(c_1174,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1166,c_150,c_974,c_758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.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 12:27:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.08/1.28 % SZS status Started for theBenchmark.p
% 2.08/1.28 % SZS status Theorem for theBenchmark.p
% 2.08/1.28
% 2.08/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.08/1.28
% 2.08/1.28 % ------ iProver source info
% 2.08/1.28
% 2.08/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.08/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.08/1.28 % git: non_committed_changes: false
% 2.08/1.28
% 2.08/1.28 % ------ Parsing...
% 2.08/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.08/1.28
% 2.08/1.28 % ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.08/1.28
% 2.08/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.08/1.28
% 2.08/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.08/1.28 % ------ Proving...
% 2.08/1.28 % ------ Problem Properties
% 2.08/1.28
% 2.08/1.28 %
% 2.08/1.28 % clauses 17
% 2.08/1.28 % conjectures 0
% 2.08/1.28 % EPR 5
% 2.08/1.28 % Horn 17
% 2.08/1.28 % unary 13
% 2.08/1.28 % binary 3
% 2.08/1.28 % lits 22
% 2.08/1.28 % lits eq 8
% 2.08/1.28 % fd_pure 0
% 2.08/1.28 % fd_pseudo 0
% 2.08/1.28 % fd_cond 0
% 2.08/1.28 % fd_pseudo_cond 0
% 2.08/1.28 % AC symbols 0
% 2.08/1.28
% 2.08/1.28 % ------ Schedule dynamic 5 is on
% 2.08/1.28
% 2.08/1.28 % ------ no conjectures: strip conj schedule
% 2.08/1.28
% 2.08/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.08/1.28
% 2.08/1.28
% 2.08/1.28 % ------
% 2.08/1.28 % Current options:
% 2.08/1.28 % ------
% 2.08/1.28
% 2.08/1.28
% 2.08/1.28 %
% 2.08/1.28
% 2.08/1.28 % ------ Proving...
% 2.08/1.28 %
% 2.08/1.28
% 2.08/1.28 % SZS status Theorem for theBenchmark.p
% 2.08/1.28
% 2.08/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.08/1.28
% 2.08/1.28
%------------------------------------------------------------------------------