%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET621+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 : n016.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 02:17:44 PM UTC 2026
% Result : Theorem 0.14s 0.84s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th97,conjecture,
! [X1,X2,X3] : difference(symmetric_difference(X1,X2),X3) = union(difference(X1,union(X2,X3)),difference(X2,union(X1,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th97) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(difference_difference_union,axiom,
! [X1,X2,X3] : difference(difference(X1,X2),X3) = difference(X1,union(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union) ).
fof(difference_distributes_over_union,axiom,
! [X1,X2,X3] : difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] : difference(symmetric_difference(X1,X2),X3) = union(difference(X1,union(X2,X3)),difference(X2,union(X1,X3))),
inference(assume_negation,[status(cth)],[prove_th97]) ).
fof(c_0_5,negated_conjecture,
difference(symmetric_difference(esk3_0,esk4_0),esk5_0) != union(difference(esk3_0,union(esk4_0,esk5_0)),difference(esk4_0,union(esk3_0,esk5_0))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X4,X5] : symmetric_difference(X4,X5) = union(difference(X4,X5),difference(X5,X4)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_0_7,negated_conjecture,
difference(symmetric_difference(esk3_0,esk4_0),esk5_0) != union(difference(esk3_0,union(esk4_0,esk5_0)),difference(esk4_0,union(esk3_0,esk5_0))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X6,X7,X8] : difference(difference(X6,X7),X8) = difference(X6,union(X7,X8)),
inference(variable_rename,[status(thm)],[difference_difference_union]) ).
cnf(c_0_10,negated_conjecture,
difference(union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)),esk5_0) != union(difference(esk3_0,union(esk4_0,esk5_0)),difference(esk4_0,union(esk3_0,esk5_0))),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
difference(difference(X1,X2),X3) = difference(X1,union(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X9,X10,X11] : difference(union(X9,X10),X11) = union(difference(X9,X11),difference(X10,X11)),
inference(variable_rename,[status(thm)],[difference_distributes_over_union]) ).
cnf(c_0_13,negated_conjecture,
union(difference(difference(esk3_0,esk4_0),esk5_0),difference(difference(esk4_0,esk3_0),esk5_0)) != difference(union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)),esk5_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_14,plain,
difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.77 % Computer : n016.cluster.edu
% 0.10/0.77 % Model : x86_64 x86_64
% 0.10/0.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.77 % Memory : 8046.5625MB
% 0.10/0.77 % OS : Linux 6.8.0-71-generic
% 0.10/0.77 % CPULimit : 300
% 0.10/0.77 % WCLimit : 300
% 0.10/0.77 % DateTime : Mon Sep 21 05:34:53 UTC 2026
% 0.10/0.78 % CPUTime :
% 0.10/0.78 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.82 Running first-order theorem proving
% 0.14/0.82 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
% 0.14/0.84 % Version: 3.5.1
% 0.14/0.84 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.84 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.84 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.84 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.84 % Starting sh5l with 300s (1) cores
% 0.14/0.84 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1657225 completed with status 0
% 0.14/0.84 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.84 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.84 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.84 % No SInE strategy applied
% 0.14/0.84 % Search class: FGHSM-FFSF22-MFFFFFNN
% 0.14/0.84 % partial match(1): FGHSM-FFMF22-MFFFFFNN
% 0.14/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.84 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.84 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.84 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.84 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.84 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.84 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1657231 completed with status 0
% 0.14/0.84 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.84 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.84 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.84 % No SInE strategy applied
% 0.14/0.84 % Search class: FGHSM-FFSF22-MFFFFFNN
% 0.14/0.84 % partial match(1): FGHSM-FFMF22-MFFFFFNN
% 0.14/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.84 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.84 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.84 % Preprocessing time : 0.002 s
% 0.14/0.84 % Presaturation interreduction done
% 0.14/0.84
% 0.14/0.84 % Proof found!
% 0.14/0.84 % SZS status Theorem
% 0.14/0.84 % SZS output start CNFRefutation
% See solution above
% 0.14/0.84 % Parsed axioms : 12
% 0.14/0.84 % Removed by relevancy pruning/SinE : 0
% 0.14/0.84 % Initial clauses : 23
% 0.14/0.84 % Removed in clause preprocessing : 3
% 0.14/0.84 % Initial clauses in saturation : 20
% 0.14/0.84 % Processed clauses : 15
% 0.14/0.84 % ...of these trivial : 0
% 0.14/0.84 % ...subsumed : 0
% 0.14/0.84 % ...remaining for further processing : 15
% 0.14/0.84 % Other redundant clauses eliminated : 2
% 0.14/0.84 % Clauses deleted for lack of memory : 0
% 0.14/0.84 % Backward-subsumed : 0
% 0.14/0.84 % Backward-rewritten : 2
% 0.14/0.84 % Generated clauses : 2
% 0.14/0.84 % ...of the previous two non-redundant : 1
% 0.14/0.84 % ...aggressively subsumed : 0
% 0.14/0.84 % Contextual simplify-reflections : 0
% 0.14/0.84 % Paramodulations : 0
% 0.14/0.84 % Factorizations : 0
% 0.14/0.84 % NegExts : 0
% 0.14/0.84 % Equation resolutions : 2
% 0.14/0.84 % Disequality decompositions : 0
% 0.14/0.84 % Total rewrite steps : 5
% 0.14/0.84 % ...of those cached : 1
% 0.14/0.84 % Propositional unsat checks : 0
% 0.14/0.84 % Propositional check models : 0
% 0.14/0.84 % Propositional check unsatisfiable : 0
% 0.14/0.84 % Propositional clauses : 0
% 0.14/0.84 % Propositional clauses after purity: 0
% 0.14/0.84 % Propositional unsat core size : 0
% 0.14/0.84 % Propositional preprocessing time : 0.000
% 0.14/0.84 % Propositional encoding time : 0.000
% 0.14/0.84 % Propositional solver time : 0.000
% 0.14/0.84 % Success case prop preproc time : 0.000
% 0.14/0.84 % Success case prop encoding time : 0.000
% 0.14/0.84 % Success case prop solver time : 0.000
% 0.14/0.84 % Current number of processed clauses : 11
% 0.14/0.84 % Positive orientable unit clauses : 3
% 0.14/0.84 % Positive unorientable unit clauses: 1
% 0.14/0.84 % Negative unit clauses : 0
% 0.14/0.84 % Non-unit-clauses : 7
% 0.14/0.84 % Current number of unprocessed clauses: 6
% 0.14/0.84 % ...number of literals in the above : 15
% 0.14/0.84 % Current number of archived formulas : 0
% 0.14/0.84 % Current number of archived clauses : 3
% 0.14/0.84 % Clause-clause subsumption calls (NU) : 4
% 0.14/0.84 % Rec. Clause-clause subsumption calls : 4
% 0.14/0.84 % Non-unit clause-clause subsumptions : 0
% 0.14/0.84 % Unit Clause-clause subsumption calls : 0
% 0.14/0.84 % Rewrite failures with RHS unbound : 0
% 0.14/0.84 % BW rewrite match attempts : 8
% 0.14/0.84 % BW rewrite match successes : 7
% 0.14/0.84 % Condensation attempts : 0
% 0.14/0.84 % Condensation successes : 0
% 0.14/0.84 % Termbank termtop insertions : 1325
% 0.14/0.84 % Search garbage collected termcells : 308
% 0.14/0.84
% 0.14/0.84 % -------------------------------------------------
% 0.14/0.84 % User time : 0.006 s
% 0.14/0.84 % System time : 0.003 s
% 0.14/0.84 % Total time : 0.009 s
% 0.14/0.84 % Maximum resident set size: 3384 pages
% 0.14/0.84
% 0.14/0.84 % -------------------------------------------------
% 0.14/0.84 % User time : 0.014 s
% 0.14/0.84 % System time : 0.011 s
% 0.14/0.84 % Total time : 0.025 s
% 0.14/0.84 % Maximum resident set size: 4608 pages
% 0.14/0.84 % E exiting
%------------------------------------------------------------------------------