%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 : Thu Sep 24 02:14:40 PM UTC 2026
% Result : Theorem 1.44s 0.63s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 4 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_distributes_over_intersection,axiom,
! [X1,X2,X3] : union(X1,intersection(X2,X3)) = intersection(union(X1,X2),union(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_distributes_over_intersection) ).
fof(union_intersection,axiom,
! [X1,X2] : union(X1,intersection(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection) ).
fof(associativity_of_intersection,axiom,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(prove_th72,conjecture,
! [X1,X2,X3] : union(union(intersection(X1,X2),intersection(X2,X3)),intersection(X3,X1)) = intersection(intersection(union(X1,X2),union(X2,X3)),union(X3,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th72) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(associativity_of_union,axiom,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_union) ).
fof(idempotency_of_intersection,axiom,
! [X1] : intersection(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_intersection) ).
fof(c_0_8,plain,
! [X13,X14,X15] : union(X13,intersection(X14,X15)) = intersection(union(X13,X14),union(X13,X15)),
inference(variable_rename,[status(thm)],[union_distributes_over_intersection]) ).
fof(c_0_9,plain,
! [X11,X12] : union(X11,intersection(X11,X12)) = X11,
inference(variable_rename,[status(thm)],[union_intersection]) ).
fof(c_0_10,plain,
! [X8,X9,X10] : intersection(intersection(X8,X9),X10) = intersection(X8,intersection(X9,X10)),
inference(variable_rename,[status(thm)],[associativity_of_intersection]) ).
cnf(c_0_11,plain,
union(X1,intersection(X2,X3)) = intersection(union(X1,X2),union(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
union(X1,intersection(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X24,X25] : union(X24,X25) = union(X25,X24),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2,X3] : union(union(intersection(X1,X2),intersection(X2,X3)),intersection(X3,X1)) = intersection(intersection(union(X1,X2),union(X2,X3)),union(X3,X1)),
inference(assume_negation,[status(cth)],[prove_th72]) ).
cnf(c_0_16,plain,
intersection(X1,union(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_12]) ).
cnf(c_0_17,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,negated_conjecture,
union(union(intersection(esk3_0,esk4_0),intersection(esk4_0,esk5_0)),intersection(esk5_0,esk3_0)) != intersection(intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk3_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_19,plain,
! [X26,X27] : intersection(X26,X27) = intersection(X27,X26),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_20,plain,
! [X4,X5,X6] : union(union(X4,X5),X6) = union(X4,union(X5,X6)),
inference(variable_rename,[status(thm)],[associativity_of_union]) ).
cnf(c_0_21,plain,
intersection(X1,union(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
union(union(intersection(esk3_0,esk4_0),intersection(esk4_0,esk5_0)),intersection(esk5_0,esk3_0)) != intersection(intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
intersection(union(X1,X2),union(X3,X1)) = union(X1,intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_26,plain,
intersection(X1,intersection(union(X2,X1),X3)) = intersection(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
intersection(union(esk3_0,esk4_0),intersection(union(esk3_0,esk5_0),union(esk4_0,esk5_0))) != union(intersection(esk3_0,esk4_0),union(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_17]),c_0_13]),c_0_23]),c_0_23]),c_0_24]),c_0_17]) ).
cnf(c_0_28,plain,
intersection(union(X1,X2),union(X3,X2)) = union(X2,intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_29,plain,
intersection(X1,union(X2,intersection(X1,X3))) = intersection(X1,union(X2,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_11]) ).
fof(c_0_30,plain,
! [X7] : intersection(X7,X7) = X7,
inference(variable_rename,[status(thm)],[idempotency_of_intersection]) ).
cnf(c_0_31,negated_conjecture,
intersection(union(esk3_0,esk4_0),union(esk5_0,intersection(esk3_0,esk4_0))) != union(intersection(esk3_0,esk4_0),union(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
intersection(X1,union(X2,X3)) = union(intersection(X1,X3),intersection(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_12]),c_0_29]) ).
cnf(c_0_33,plain,
intersection(X1,intersection(X2,X3)) = intersection(X3,intersection(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_34,plain,
intersection(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_23]),c_0_32]),c_0_34]),c_0_17]),c_0_12]),c_0_23]),c_0_23]),c_0_32]),c_0_23]),c_0_23]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n017.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 : Mon Sep 21 05:23:26 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.44/0.63 % Version: 3.5.1
% 1.44/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.44/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.44/0.63 % Starting new_bool_3 with 300s (1) cores
% 1.44/0.63 % Starting new_bool_1 with 300s (1) cores
% 1.44/0.63 % Starting sh5l with 300s (1) cores
% 1.44/0.63 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1514114 completed with status 0
% 1.44/0.63 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.44/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.44/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.44/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.44/0.63 % No SInE strategy applied
% 1.44/0.63 % Search class: FGUSM-FFMF22-MFFFFFNN
% 1.44/0.63 % partial match(1): FGUSM-FFMF21-MFFFFFNN
% 1.44/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.44/0.63 % Starting SubtermCWHack with 136s (1) cores
% 1.44/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.44/0.63 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 1.44/0.63 % Starting new_bool_3 with 136s (1) cores
% 1.44/0.63 % Starting new_bool_1 with 136s (1) cores
% 1.44/0.63 % G-E--_200_B02_F1_AE_CS_SP_PI_S0S with pid 1514121 completed with status 0
% 1.44/0.63 % Result found by G-E--_200_B02_F1_AE_CS_SP_PI_S0S
% 1.44/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.44/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.44/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.44/0.63 % No SInE strategy applied
% 1.44/0.63 % Search class: FGUSM-FFMF22-MFFFFFNN
% 1.44/0.63 % partial match(1): FGUSM-FFMF21-MFFFFFNN
% 1.44/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.44/0.63 % Starting SubtermCWHack with 136s (1) cores
% 1.44/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.44/0.63 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 1.44/0.63 % Preprocessing time : 0.001 s
% 1.44/0.63
% 1.44/0.63 % Proof found!
% 1.44/0.63 % SZS status Theorem
% 1.44/0.63 % SZS output start CNFRefutation
% See solution above
% 1.44/0.63 % Parsed axioms : 14
% 1.44/0.63 % Removed by relevancy pruning/SinE : 0
% 1.44/0.63 % Initial clauses : 25
% 1.44/0.63 % Removed in clause preprocessing : 2
% 1.44/0.63 % Initial clauses in saturation : 23
% 1.44/0.63 % Processed clauses : 1486
% 1.44/0.63 % ...of these trivial : 212
% 1.44/0.63 % ...subsumed : 1084
% 1.44/0.63 % ...remaining for further processing : 190
% 1.44/0.63 % Other redundant clauses eliminated : 2
% 1.44/0.63 % Clauses deleted for lack of memory : 0
% 1.44/0.63 % Backward-subsumed : 0
% 1.44/0.63 % Backward-rewritten : 43
% 1.44/0.63 % Generated clauses : 16325
% 1.44/0.63 % ...of the previous two non-redundant : 12433
% 1.44/0.63 % ...aggressively subsumed : 0
% 1.44/0.63 % Contextual simplify-reflections : 0
% 1.44/0.63 % Paramodulations : 16283
% 1.44/0.63 % Factorizations : 40
% 1.44/0.63 % NegExts : 0
% 1.44/0.63 % Equation resolutions : 2
% 1.44/0.63 % Disequality decompositions : 0
% 1.44/0.63 % Total rewrite steps : 15776
% 1.44/0.63 % ...of those cached : 10920
% 1.44/0.63 % Propositional unsat checks : 0
% 1.44/0.63 % Propositional check models : 0
% 1.44/0.63 % Propositional check unsatisfiable : 0
% 1.44/0.63 % Propositional clauses : 0
% 1.44/0.63 % Propositional clauses after purity: 0
% 1.44/0.63 % Propositional unsat core size : 0
% 1.44/0.63 % Propositional preprocessing time : 0.000
% 1.44/0.63 % Propositional encoding time : 0.000
% 1.44/0.63 % Propositional solver time : 0.000
% 1.44/0.63 % Success case prop preproc time : 0.000
% 1.44/0.63 % Success case prop encoding time : 0.000
% 1.44/0.63 % Success case prop solver time : 0.000
% 1.44/0.63 % Current number of processed clauses : 145
% 1.44/0.63 % Positive orientable unit clauses : 60
% 1.44/0.63 % Positive unorientable unit clauses: 9
% 1.44/0.63 % Negative unit clauses : 0
% 1.44/0.63 % Non-unit-clauses : 76
% 1.44/0.63 % Current number of unprocessed clauses: 10898
% 1.44/0.63 % ...number of literals in the above : 19809
% 1.44/0.63 % Current number of archived formulas : 0
% 1.44/0.63 % Current number of archived clauses : 43
% 1.44/0.63 % Clause-clause subsumption calls (NU) : 4523
% 1.44/0.63 % Rec. Clause-clause subsumption calls : 4385
% 1.44/0.63 % Non-unit clause-clause subsumptions : 724
% 1.44/0.63 % Unit Clause-clause subsumption calls : 65
% 1.44/0.63 % Rewrite failures with RHS unbound : 206
% 1.44/0.63 % BW rewrite match attempts : 515
% 1.44/0.63 % BW rewrite match successes : 268
% 1.44/0.63 % Condensation attempts : 0
% 1.44/0.63 % Condensation successes : 0
% 1.44/0.63 % Termbank termtop insertions : 163450
% 1.44/0.63 % Search garbage collected termcells : 317
% 1.44/0.63
% 1.44/0.63 % -------------------------------------------------
% 1.44/0.63 % User time : 0.181 s
% 1.44/0.63 % System time : 0.015 s
% 1.44/0.63 % Total time : 0.197 s
% 1.44/0.63 % Maximum resident set size: 3384 pages
% 1.44/0.63
% 1.44/0.63 % -------------------------------------------------
% 1.44/0.63 % User time : 0.916 s
% 1.44/0.63 % System time : 0.077 s
% 1.44/0.63 % Total time : 0.993 s
% 1.44/0.63 % Maximum resident set size: 4608 pages
% 1.44/0.63 % E exiting
%------------------------------------------------------------------------------