%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG006-1 : 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 : n003.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 0.68s 1.20s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 66 ( 66 unt; 0 def)
% Number of atoms : 101 ( 65 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 146 ( 0 sgn 146 !; 0 ?; 139 :)
% 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),difference(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_3) ).
fof(f4,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_difference_3_simplified) ).
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),difference(X2,X1)) = difference(difference(X0,X2),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
inference(cnf_transformation,[],[f4]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),X1) = difference(X0,X1),
inference(superposition,[status(thm)],[c_53,c_53]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),difference(X1,difference(X1,X0))) = difference(X0,X1),
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X2,X0)) = difference(X0,difference(X1,difference(X2,X0))),
inference(superposition,[status(thm)],[c_53,c_55]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X2)),X2) = difference(difference(X0,X2),difference(X1,X2)),
inference(superposition,[status(thm)],[c_53,c_55]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : difference(difference(X0,difference(X0,X1)),X1) = difference(X1,difference(X1,difference(X0,X1))),
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] : difference(difference(X0,difference(X0,X1)),X1) = difference(X1,X1),
inference(demodulation,[status(thm)],[c_81,c_53]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X2)),X2) = difference(difference(X0,X1),X2),
inference(demodulation,[status(thm)],[c_73,c_55]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X1),X2),X1) = difference(difference(X0,X1),difference(X2,X1)),
inference(superposition,[status(thm)],[c_63,c_55]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X1),difference(difference(X0,X2),X1)),difference(X2,X1)) = difference(difference(X2,X1),difference(X2,X1)),
inference(superposition,[status(thm)],[c_55,c_84]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,difference(X0,X1)),X2),X1) = difference(difference(X1,X1),difference(X2,X1)),
inference(superposition,[status(thm)],[c_84,c_55]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X0),X1) = difference(X1,X1),
inference(demodulation,[status(thm)],[c_84,c_85]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X1),X2),X1) = difference(difference(X0,X2),X1),
inference(demodulation,[status(thm)],[c_101,c_55]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,difference(X0,X1)),X2),X1) = difference(X1,X1),
inference(demodulation,[status(thm)],[c_149,c_53,c_69]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X0),X1),X2) = difference(difference(X1,X1),X2),
inference(demodulation,[status(thm)],[c_142,c_55,c_85]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i] : difference(difference(X0,difference(X1,X1)),difference(difference(X1,X1),difference(X0,X0))) = difference(X0,difference(X1,X1)),
inference(superposition,[status(thm)],[c_176,c_65]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X1)),X2) = difference(difference(X0,X2),difference(X2,X2)),
inference(superposition,[status(thm)],[c_176,c_55]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i] : difference(difference(difference(X0,X1),X0),X1) = difference(X1,X1),
inference(superposition,[status(thm)],[c_176,c_85]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(difference(X2,X2),X1)) = difference(difference(X0,X1),X1),
inference(superposition,[status(thm)],[c_176,c_55]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X0),difference(X1,X2)) = difference(difference(X1,X1),X2),
inference(superposition,[status(thm)],[c_176,c_55]) ).
tcf(c_327,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X0),X1) = difference(difference(X2,X2),X1),
inference(superposition,[status(thm)],[c_176,c_176]) ).
tcf(c_475,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),X0) = difference(X0,X0),
inference(superposition,[status(thm)],[c_53,c_184]) ).
tcf(c_476,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,difference(X0,X1)),X2),X0) = difference(X0,X0),
inference(superposition,[status(thm)],[c_54,c_184]) ).
tcf(c_585,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X0),X1) = difference(difference(X1,X0),X1),
inference(superposition,[status(thm)],[c_188,c_181]) ).
tcf(c_631,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X0),X1) = iPr_def_10(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_327]) ).
tcf(c_633,plain,
! [X0: $i] : difference(X0,X0) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_316,c_475,c_631]) ).
tcf(c_635,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,difference(X0,X1)),X2),X0) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_476,c_633]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i] : iPr_def_10(difference(X0,X1)) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_324,c_631]) ).
tcf(c_657,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),iPr_def_10(X1)) = difference(difference(X0,X1),X1),
inference(demodulation,[status(thm)],[c_323,c_631]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),iPr_def_10(X1)) = difference(X0,X1),
inference(demodulation,[status(thm)],[c_657,c_63]) ).
tcf(c_660,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,iPr_def_10(X1)),X2) = difference(X0,X2),
inference(demodulation,[status(thm)],[c_313,c_633,c_658]) ).
tcf(c_705,plain,
! [X0: $i,X1: $i] : difference(X0,iPr_def_10(X0)) = difference(X0,iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_305,c_631,c_633,c_639,c_660]) ).
tcf(c_1318,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X2)),X1) = difference(difference(X0,X1),difference(X1,X1)),
inference(superposition,[status(thm)],[c_475,c_55]) ).
tcf(c_1374,plain,
! [X0: $i,X1: $i] : difference(iPr_def_10(X0),difference(X1,iPr_def_10(X1))) = iPr_def_10(X0),
inference(superposition,[status(thm)],[c_705,c_53]) ).
tcf(c_1528,plain,
! [X0: $i,X1: $i] : difference(difference(iPr_def_10(X0),iPr_def_10(X0)),X1) = difference(X1,X1),
inference(superposition,[status(thm)],[c_585,c_660]) ).
tcf(c_1550,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),X0) = iPr_def_10(X0),
inference(superposition,[status(thm)],[c_53,c_635]) ).
tcf(c_1579,plain,
! [X0: $i] : difference(X0,iPr_def_10(X0)) = X0,
inference(superposition,[status(thm)],[c_635,c_53]) ).
tcf(c_1614,plain,
! [X0: $i,X1: $i] : difference(iPr_def_10(X0),X1) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_1374,c_1579]) ).
tcf(c_1627,plain,
! [X0: $i,X1: $i] : difference(X0,X0) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_1528,c_1614]) ).
tcf(c_1689,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X2)),X1) = difference(X0,X1),
inference(demodulation,[status(thm)],[c_1318,c_55,c_63]) ).
tcf(c_1782,plain,
! [X0: $i,X1: $i] : difference(X0,iPr_def_10(X1)) = X0,
inference(demodulation,[status(thm)],[c_705,c_1579]) ).
tcf(c_1822,plain,
! [X0: $i,X1: $i] : difference(X0,X0) = difference(X1,X1),
inference(superposition,[status(thm)],[c_1627,c_1627]) ).
tcf(c_1830,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X1,X1)) = X0,
inference(superposition,[status(thm)],[c_1627,c_1782]) ).
tcf(c_1836,plain,
! [X0: $i,X1: $i] : difference(X0,difference(iPr_def_10(X1),difference(iPr_def_10(X1),X0))) = X0,
inference(superposition,[status(thm)],[c_1782,c_65]) ).
tcf(c_1849,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X0),X1) = difference(X0,X0),
inference(superposition,[status(thm)],[c_1627,c_1614]) ).
tcf(c_1890,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X0,difference(X0,X1))) = difference(difference(X0,X1),iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_1550,c_54]) ).
tcf(c_2000,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X0,difference(X1,X2))) = iPr_def_10(difference(X0,difference(X1,X2))),
inference(superposition,[status(thm)],[c_1689,c_1550]) ).
tcf(c_2079,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X0,difference(X0,X0))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_69,c_1627]) ).
tcf(c_2085,plain,
! [X0: $i] : difference(X0,X0) = iPr_def_12,
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_1822]) ).
tcf(c_2091,plain,
! [X0: $i] : difference(iPr_def_12,X0) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1849,c_2085]) ).
tcf(c_2092,plain,
! [X0: $i] : iPr_def_10(X0) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2079,c_1830,c_2085]) ).
tcf(c_2095,plain,
! [X0: $i] : difference(X0,iPr_def_12) = X0,
inference(demodulation,[status(thm)],[c_1836,c_2091,c_2092]) ).
tcf(c_2114,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X0,difference(X0,X1))) = difference(X0,X1),
inference(demodulation,[status(thm)],[c_1890,c_2092,c_2095]) ).
tcf(c_2129,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X0,difference(X1,X2))) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2000,c_2092]) ).
tcf(c_2911,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X1),X2),difference(difference(difference(X0,X1),X2),difference(difference(X0,X2),X1))) = difference(difference(X0,X2),X1),
inference(superposition,[status(thm)],[c_181,c_2114]) ).
tcf(c_2958,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X1),X2),difference(difference(X0,X2),X1)) = iPr_def_12,
inference(superposition,[status(thm)],[c_55,c_2129]) ).
tcf(c_3018,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X1),X2),iPr_def_12) = difference(difference(X0,X2),X1),
inference(demodulation,[status(thm)],[c_2911,c_2958]) ).
tcf(c_3019,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),X1),
inference(demodulation,[status(thm)],[c_3018,c_2095]) ).
tcf(c_3024,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_3019]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG006-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 04:32:23 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 Running UEQ theorem proving
% 0.14/0.42 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
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 0.68/1.20 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 0.68/1.20 % SZS status Started for theBenchmark.p
% 0.68/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 0.68/1.20
% 0.68/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.68/1.20
% 0.68/1.20 % ------ iProver source info
% 0.68/1.20
% 0.68/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 0.68/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.68/1.20 % git: non_committed_changes: false
% 0.68/1.20
% 0.68/1.20 % ------ Parsing...% successful
% 0.68/1.20
% 0.68/1.20
% 0.68/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.68/1.20 % ------ Proving...
% 0.68/1.20 % ------ Problem Properties
% 0.68/1.20
% 0.68/1.20 %
% 0.68/1.20 % clauses 4
% 0.68/1.20 % conjectures 1
% 0.68/1.20 % EPR 0
% 0.68/1.20 % Horn 4
% 0.68/1.20 % unary 4
% 0.68/1.20 % binary 0
% 0.68/1.20 % lits 4
% 0.68/1.20 % lits eq 4
% 0.68/1.20 % fd_pure 0
% 0.68/1.20 % fd_pseudo 0
% 0.68/1.20 % fd_cond 0
% 0.68/1.20 % fd_pseudo_cond 0
% 0.68/1.20 % AC symbols 0
% 0.68/1.20
% 0.68/1.20 % ------ Input Options Time Limit: Unbounded
% 0.68/1.20
% 0.68/1.20
% 0.68/1.20 % ------
% 0.68/1.20 % Current options:
% 0.68/1.20 % ------
% 0.68/1.20
% 0.68/1.20
% 0.68/1.20 %
% 0.68/1.20
% 0.68/1.20 % ------ Proving...
% 0.68/1.20 %
% 0.68/1.20
% 0.68/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 0.68/1.20
% 0.68/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.68/1.21
% 0.68/1.21
%------------------------------------------------------------------------------