%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG007-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 12:53:09 PM UTC 2026
% Result : Unsatisfiable 9.56s 2.67s
% Output : CNFRefutation 9.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 64 ( 64 unt; 5 def)
% Number of atoms : 209 ( 63 equ)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : difference(X0,difference(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_1) ).
fof(f2,axiom,
! [X0,X1] : difference(X0,difference(X0,X1)) = difference(X1,difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_2) ).
fof(f3,axiom,
! [X2,X0,X1] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_3_simplified) ).
fof(f4,negated_conjecture,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_difference_3) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X0,X1)) = difference(X1,difference(X1,X0)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
difference(difference(a,c),difference(b,c)) != difference(difference(a,b),c),
inference(cnf_transformation,[],[f4]) ).
tcf(c_71,definition,
iPr_def_10 = difference(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_72,definition,
iPr_def_11 = difference(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_73,definition,
iPr_def_12 = difference(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_74,definition,
iPr_def_13 = difference(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_75,definition,
iPr_def_14 = difference(iPr_def_13,c),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_76,negated_conjecture,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_56,c_74,c_75,c_72,c_71,c_73]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),X1),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X0,X1)) = difference(X1,difference(X1,X0)),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_118,plain,
difference(b,iPr_def_13) = b,
inference(superposition,[status(thm)],[c_74,c_79]) ).
tcf(c_121,plain,
difference(iPr_def_11,iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_73,c_79]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),X1) = difference(X0,X1),
inference(superposition,[status(thm)],[c_79,c_79]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X2,X0)) = difference(X0,X1),
inference(superposition,[status(thm)],[c_79,c_77]) ).
tcf(c_136,plain,
! [X0: $i] : difference(difference(a,X0),c) = difference(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_71,c_77]) ).
tcf(c_137,plain,
! [X0: $i] : difference(difference(b,X0),c) = difference(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_72,c_77]) ).
tcf(c_139,plain,
! [X0: $i] : difference(difference(iPr_def_13,X0),c) = difference(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_75,c_77]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(difference(X1,X0),X2)) = X0,
inference(superposition,[status(thm)],[c_77,c_79]) ).
tcf(c_161,plain,
difference(b,difference(b,a)) = difference(a,iPr_def_13),
inference(superposition,[status(thm)],[c_74,c_78]) ).
tcf(c_164,plain,
difference(iPr_def_11,difference(iPr_def_11,iPr_def_10)) = difference(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_73,c_78]) ).
tcf(c_273,plain,
difference(iPr_def_11,c) = iPr_def_11,
inference(superposition,[status(thm)],[c_72,c_123]) ).
tcf(c_275,plain,
difference(iPr_def_14,c) = iPr_def_14,
inference(superposition,[status(thm)],[c_75,c_123]) ).
tcf(c_322,plain,
difference(iPr_def_10,b) = difference(iPr_def_13,c),
inference(superposition,[status(thm)],[c_74,c_136]) ).
tcf(c_338,plain,
difference(b,c) = difference(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_118,c_137]) ).
tcf(c_347,plain,
difference(b,c) = difference(iPr_def_11,c),
inference(superposition,[status(thm)],[c_137,c_123]) ).
tcf(c_377,plain,
difference(iPr_def_13,c) = difference(iPr_def_14,c),
inference(superposition,[status(thm)],[c_139,c_123]) ).
tcf(c_417,plain,
! [X0: $i] : difference(iPr_def_13,difference(b,X0)) = iPr_def_13,
inference(superposition,[status(thm)],[c_118,c_143]) ).
tcf(c_420,plain,
! [X0: $i] : difference(iPr_def_12,difference(iPr_def_11,X0)) = iPr_def_12,
inference(superposition,[status(thm)],[c_121,c_143]) ).
tcf(c_443,plain,
difference(difference(a,iPr_def_13),c) = difference(iPr_def_11,difference(b,a)),
inference(superposition,[status(thm)],[c_161,c_137]) ).
tcf(c_503,plain,
! [X0: $i] : difference(iPr_def_12,difference(X0,iPr_def_10)) = iPr_def_12,
inference(superposition,[status(thm)],[c_73,c_132]) ).
tcf(c_504,plain,
! [X0: $i] : difference(iPr_def_14,difference(X0,iPr_def_13)) = iPr_def_14,
inference(superposition,[status(thm)],[c_75,c_132]) ).
tcf(c_635,plain,
difference(iPr_def_13,c) = iPr_def_14,
inference(demodulation,[status(thm)],[c_377,c_275]) ).
tcf(c_637,plain,
difference(b,c) = iPr_def_11,
inference(demodulation,[status(thm)],[c_347,c_273]) ).
tcf(c_638,plain,
difference(iPr_def_11,iPr_def_13) = iPr_def_11,
inference(demodulation,[status(thm)],[c_338,c_637]) ).
tcf(c_640,plain,
difference(iPr_def_10,b) = iPr_def_14,
inference(demodulation,[status(thm)],[c_322,c_635]) ).
tcf(c_655,plain,
difference(iPr_def_11,difference(b,a)) = difference(iPr_def_10,iPr_def_13),
inference(demodulation,[status(thm)],[c_443,c_136]) ).
tcf(c_1070,plain,
! [X0: $i] : difference(difference(iPr_def_11,X0),iPr_def_13) = difference(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_638,c_77]) ).
tcf(c_1138,plain,
! [X0: $i] : difference(iPr_def_14,difference(X0,iPr_def_10)) = iPr_def_14,
inference(superposition,[status(thm)],[c_640,c_132]) ).
tcf(c_1167,plain,
! [X0: $i] : difference(iPr_def_13,difference(X0,difference(X0,b))) = iPr_def_13,
inference(superposition,[status(thm)],[c_78,c_417]) ).
tcf(c_1402,plain,
! [X0: $i] : difference(difference(X0,iPr_def_13),iPr_def_14) = difference(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_504,c_79]) ).
tcf(c_1860,plain,
difference(difference(iPr_def_10,iPr_def_12),iPr_def_13) = difference(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_164,c_1070]) ).
tcf(c_2033,plain,
difference(difference(iPr_def_10,iPr_def_13),iPr_def_12) = difference(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_1860,c_77]) ).
tcf(c_2289,plain,
difference(iPr_def_13,difference(iPr_def_10,iPr_def_14)) = iPr_def_13,
inference(superposition,[status(thm)],[c_640,c_1167]) ).
tcf(c_2582,plain,
difference(difference(iPr_def_10,iPr_def_14),iPr_def_13) = difference(iPr_def_10,iPr_def_14),
inference(superposition,[status(thm)],[c_2289,c_79]) ).
tcf(c_2684,plain,
difference(iPr_def_10,iPr_def_13) = difference(iPr_def_10,iPr_def_14),
inference(demodulation,[status(thm)],[c_2582,c_77,c_1402]) ).
tcf(c_2819,plain,
difference(iPr_def_10,difference(iPr_def_10,iPr_def_13)) = difference(iPr_def_14,difference(iPr_def_14,iPr_def_10)),
inference(superposition,[status(thm)],[c_2684,c_78]) ).
tcf(c_3080,plain,
difference(iPr_def_13,difference(iPr_def_13,iPr_def_10)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_2819,c_78,c_1138]) ).
tcf(c_5126,plain,
difference(iPr_def_12,difference(iPr_def_10,iPr_def_13)) = iPr_def_12,
inference(superposition,[status(thm)],[c_655,c_420]) ).
tcf(c_7112,plain,
! [X0: $i] : difference(difference(difference(iPr_def_10,iPr_def_13),X0),iPr_def_12) = difference(difference(iPr_def_10,iPr_def_13),X0),
inference(superposition,[status(thm)],[c_5126,c_132]) ).
tcf(c_11453,plain,
! [X0: $i] : difference(difference(iPr_def_10,iPr_def_12),difference(X0,difference(iPr_def_10,iPr_def_13))) = difference(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_2033,c_132]) ).
tcf(c_11456,plain,
! [X0: $i] : difference(difference(difference(iPr_def_10,iPr_def_13),X0),iPr_def_12) = difference(difference(iPr_def_10,iPr_def_12),X0),
inference(superposition,[status(thm)],[c_2033,c_77]) ).
tcf(c_11585,plain,
! [X0: $i] : difference(difference(iPr_def_10,iPr_def_12),X0) = difference(difference(iPr_def_10,iPr_def_13),X0),
inference(demodulation,[status(thm)],[c_11456,c_7112]) ).
tcf(c_11586,plain,
! [X0: $i] : difference(difference(iPr_def_10,iPr_def_13),difference(X0,difference(iPr_def_10,iPr_def_13))) = difference(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_11453,c_11585]) ).
tcf(c_11587,plain,
difference(iPr_def_10,iPr_def_12) = difference(iPr_def_10,iPr_def_13),
inference(demodulation,[status(thm)],[c_11586,c_79]) ).
tcf(c_12179,plain,
difference(iPr_def_10,difference(iPr_def_10,iPr_def_13)) = difference(iPr_def_12,difference(iPr_def_12,iPr_def_10)),
inference(superposition,[status(thm)],[c_11587,c_78]) ).
tcf(c_12202,plain,
iPr_def_12 = iPr_def_14,
inference(demodulation,[status(thm)],[c_12179,c_78,c_503,c_3080]) ).
tcf(c_12203,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12202,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG007-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.64 % Computer : n013.cluster.edu
% 0.17/0.64 % Model : x86_64 x86_64
% 0.17/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.64 % Memory : 8046.5625MB
% 0.17/0.64 % OS : Linux 6.8.0-71-generic
% 0.17/0.64 % CPULimit : 300
% 0.17/0.64 % WCLimit : 300
% 0.17/0.64 % DateTime : Fri Sep 25 04:30:21 UTC 2026
% 0.17/0.65 % CPUTime :
% 0.17/0.65 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/0.70 Running UEQ theorem proving
% 0.22/0.70 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.72
% 0.22/0.72 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.72
% 0.22/0.72 % Detected problem language: tptp
% 0.22/0.74 % Proving...
% 9.56/2.67 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 9.56/2.67 % SZS status Started for theBenchmark.p
% 9.56/2.67 % SZS status Unsatisfiable for theBenchmark.p
% 9.56/2.67
% 9.56/2.67 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.56/2.67
% 9.56/2.67 % ------ iProver source info
% 9.56/2.67
% 9.56/2.67 % git: date: 2026-07-19 20:42:38 +0200
% 9.56/2.67 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.56/2.67 % git: non_committed_changes: false
% 9.56/2.67
% 9.56/2.67 % ------ Parsing...% successful
% 9.56/2.67
% 9.56/2.67
% 9.56/2.67 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.56/2.67
% 9.56/2.67 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 9.56/2.67
% 9.56/2.67 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.56/2.67
% 9.56/2.67 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 9.56/2.67 % ------ Proving...
% 9.56/2.67 % ------ Problem Properties
% 9.56/2.67
% 9.56/2.67 %
% 9.56/2.67 % clauses 9
% 9.56/2.67 % conjectures 1
% 9.56/2.67 % EPR 1
% 9.56/2.67 % Horn 9
% 9.56/2.67 % unary 9
% 9.56/2.67 % binary 0
% 9.56/2.67 % lits 9
% 9.56/2.67 % lits eq 9
% 9.56/2.67 % fd_pure 0
% 9.56/2.67 % fd_pseudo 0
% 9.56/2.67 % fd_cond 0
% 9.56/2.67 % fd_pseudo_cond 0
% 9.56/2.67 % AC symbols 0
% 9.56/2.67
% 9.56/2.67 % ------ Input Options Time Limit: Unbounded
% 9.56/2.67
% 9.56/2.67
% 9.56/2.67 % ------
% 9.56/2.67 % Current options:
% 9.56/2.67 % ------
% 9.56/2.67
% 9.56/2.67
% 9.56/2.67 %
% 9.56/2.67
% 9.56/2.67 % ------ Proving...
% 9.56/2.67 %
% 9.56/2.67
% 9.56/2.67 % SZS status Unsatisfiable for theBenchmark.p
% 9.56/2.67
% 9.56/2.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.56/2.67
% 9.56/2.67
%------------------------------------------------------------------------------