%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET971+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 : n014.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 02:49:14 PM UTC 2026
% Result : Theorem 2.14s 6.30s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 45 unt; 6 def)
% Number of atoms : 135 ( 55 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 32 ( 14 ~; 7 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 1 sgn 53 !; 8 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f6,axiom,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) = cartesian_product2(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) = cartesian_product2(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f10,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f2]) ).
fof(f12,plain,
? [X0,X1,X2,X3] :
( subset(X2,X3)
& subset(X0,X1)
& cartesian_product2(X0,X2) != set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
? [X0,X1,X2,X3] :
( subset(X2,X3)
& subset(X0,X1)
& cartesian_product2(X0,X2) != set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(ennf_transformation,[],[f9]) ).
fof(f17,plain,
( subset(sK4,sK5)
& subset(sK2,sK3)
& cartesian_product2(sK2,sK4) != set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f13]) ).
fof(f18,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f6]) ).
fof(f24,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
cartesian_product2(sK2,sK4) != set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4)),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_50,plain,
! [X0: $i] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_55,negated_conjecture,
set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4)) != cartesian_product2(sK2,sK4),
inference(cnf_transformation,[],[f26]) ).
tcf(c_56,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f25]) ).
tcf(c_57,negated_conjecture,
subset(sK4,sK5),
inference(cnf_transformation,[],[f24]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_58]) ).
tcf(c_102,plain,
set_intersection2(sK2,sK3) = sK2,
inference(unflattening,[status(thm)],[c_101]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ( X1 != sK5 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_58]) ).
tcf(c_107,plain,
set_intersection2(sK4,sK5) = sK4,
inference(unflattening,[status(thm)],[c_106]) ).
tcf(c_131,definition,
iPr_def_10 = set_intersection2(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_132,definition,
iPr_def_11 = set_intersection2(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_133,definition,
iPr_def_12 = cartesian_product2(sK2,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_134,definition,
iPr_def_13 = cartesian_product2(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_135,definition,
iPr_def_14 = set_intersection2(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_136,definition,
iPr_def_15 = cartesian_product2(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_137,plain,
iPr_def_10 = sK4,
inference(demodulation,[status(thm)],[c_107,c_131]) ).
tcf(c_138,plain,
iPr_def_11 = sK2,
inference(demodulation,[status(thm)],[c_102,c_132]) ).
tcf(c_139,negated_conjecture,
iPr_def_14 != iPr_def_15,
inference(demodulation,[status(thm)],[c_55,c_136,c_134,c_133,c_135]) ).
tcf(c_192,plain,
set_intersection2(iPr_def_10,sK5) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_131,c_137]) ).
tcf(c_193,plain,
set_intersection2(iPr_def_11,sK3) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_132,c_138]) ).
tcf(c_194,plain,
cartesian_product2(iPr_def_11,sK5) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_133,c_138]) ).
tcf(c_195,plain,
cartesian_product2(sK3,iPr_def_10) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_134,c_137]) ).
tcf(c_196,plain,
cartesian_product2(iPr_def_11,iPr_def_10) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_136,c_137,c_138]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i] : set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) = cartesian_product2(X0,set_intersection2(X1,X2)),
inference(superposition,[status(thm)],[c_50,c_54]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] : set_intersection2(cartesian_product2(iPr_def_11,X0),cartesian_product2(sK3,X1)) = cartesian_product2(iPr_def_11,set_intersection2(X0,X1)),
inference(superposition,[status(thm)],[c_193,c_54]) ).
tcf(c_216,plain,
! [X0: $i] : set_intersection2(iPr_def_15,cartesian_product2(iPr_def_11,X0)) = cartesian_product2(iPr_def_11,set_intersection2(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_196,c_199]) ).
tcf(c_246,plain,
! [X0: $i] : set_intersection2(iPr_def_15,cartesian_product2(iPr_def_11,X0)) = cartesian_product2(iPr_def_11,set_intersection2(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_49,c_216]) ).
tcf(c_249,plain,
set_intersection2(iPr_def_15,cartesian_product2(iPr_def_11,sK5)) = cartesian_product2(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_192,c_216]) ).
tcf(c_252,plain,
set_intersection2(iPr_def_15,iPr_def_12) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_249,c_194,c_196]) ).
tcf(c_254,plain,
set_intersection2(iPr_def_12,iPr_def_15) = iPr_def_15,
inference(demodulation,[status(thm)],[c_252,c_49]) ).
tcf(c_277,plain,
! [X0: $i] : set_intersection2(cartesian_product2(iPr_def_11,X0),iPr_def_13) = cartesian_product2(iPr_def_11,set_intersection2(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_195,c_202]) ).
tcf(c_283,plain,
! [X0: $i] : set_intersection2(cartesian_product2(iPr_def_11,X0),iPr_def_13) = set_intersection2(iPr_def_15,cartesian_product2(iPr_def_11,X0)),
inference(light_normalisation,[status(thm)],[c_277,c_246]) ).
tcf(c_350,plain,
! [X0: $i] : set_intersection2(iPr_def_13,cartesian_product2(iPr_def_11,X0)) = set_intersection2(iPr_def_15,cartesian_product2(iPr_def_11,X0)),
inference(demodulation,[status(thm)],[c_283,c_49]) ).
tcf(c_353,plain,
set_intersection2(iPr_def_13,iPr_def_12) = set_intersection2(iPr_def_15,iPr_def_12),
inference(superposition,[status(thm)],[c_194,c_350]) ).
tcf(c_361,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_353,c_49,c_135,c_254]) ).
tcf(c_362,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_361,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET971+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n014.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 12:29:37 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 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
% 0.16/5.43
% 0.16/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.43
% 0.16/5.43 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 2.14/6.30 % SZS status Started for theBenchmark.p
% 2.14/6.30 % SZS status Theorem for theBenchmark.p
% 2.14/6.30
% 2.14/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.14/6.30
% 2.14/6.30 % ------ iProver source info
% 2.14/6.30
% 2.14/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.14/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.14/6.30 % git: non_committed_changes: false
% 2.14/6.30
% 2.14/6.30 % ------ Parsing...
% 2.14/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.14/6.30
% 2.14/6.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 2.14/6.30
% 2.14/6.30 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.14/6.30 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.14/6.30
% 2.14/6.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.14/6.30 % ------ Proving...
% 2.14/6.30 % ------ Problem Properties
% 2.14/6.30
% 2.14/6.30 %
% 2.14/6.30 % clauses 13
% 2.14/6.30 % conjectures 1
% 2.14/6.30 % EPR 4
% 2.14/6.30 % Horn 13
% 2.14/6.30 % unary 13
% 2.14/6.30 % binary 0
% 2.14/6.30 % lits 13
% 2.14/6.30 % lits eq 13
% 2.14/6.30 % fd_pure 0
% 2.14/6.30 % fd_pseudo 0
% 2.14/6.30 % fd_cond 0
% 2.14/6.30 % fd_pseudo_cond 0
% 2.14/6.30 % AC symbols 0
% 2.14/6.30
% 2.14/6.30 % ------ Schedule UEQ
% 2.14/6.30
% 2.14/6.30 % ------ Option_UEQ Time Limit: 10.
% 2.14/6.30
% 2.14/6.30
% 2.14/6.30 % ------
% 2.14/6.30 % Current options:
% 2.14/6.30 % ------
% 2.14/6.30
% 2.14/6.30
% 2.14/6.30 %
% 2.14/6.30
% 2.14/6.30 % ------ Proving...
% 2.14/6.30 %
% 2.14/6.30
% 2.14/6.30 % SZS status Theorem for theBenchmark.p
% 2.14/6.30
% 2.14/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.14/6.30
% 2.14/6.30
%------------------------------------------------------------------------------