%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 02:23:54 PM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 110 ( 26 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 117 ( 47 ~; 51 |; 11 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 8 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(l32_xboole_1,conjecture,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_7,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ( X20 = set_difference(X18,X19)
| in(esk2_3(X18,X19,X20),X20)
| ~ in(esk2_3(X18,X19,X20),X19) )
& ( X20 = set_difference(X18,X19)
| in(esk2_3(X18,X19,X20),X20)
| in(esk2_3(X18,X19,X20),X18) )
& ( X20 = set_difference(X18,X19)
| in(esk2_3(X18,X19,X20),X19)
| ~ in(esk2_3(X18,X19,X20),X18)
| ~ in(esk2_3(X18,X19,X20),X20) )
& ( X15 != set_difference(X13,X14)
| in(X17,X15)
| in(X17,X14)
| ~ in(X17,X13) )
& ( X15 != set_difference(X13,X14)
| ~ in(X16,X15)
| ~ in(X16,X14) )
& ( X15 != set_difference(X13,X14)
| ~ in(X16,X15)
| in(X16,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])])]) ).
cnf(c_0_8,plain,
( X3 != set_difference(X4,X2)
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_9,plain,
! [X31] : set_difference(empty_set,X31) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
cnf(c_0_10,plain,
( ~ in(X1,X3)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X7,X8,X9,X10,X11] :
( ( subset(X10,X11)
| ~ in(esk1_2(X10,X11),X11) )
& ( subset(X10,X11)
| in(esk1_2(X10,X11),X10) )
& ( in(X9,X8)
| ~ in(X9,X7)
| ~ subset(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])]) ).
cnf(c_0_13,plain,
( ~ in(X1,X2)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[l32_xboole_1]) ).
cnf(c_0_16,plain,
( ~ in(esk1_2(empty_set,X1),X2)
| subset(empty_set,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_17,negated_conjecture,
( ( subset(esk3_0,esk4_0)
| set_difference(esk3_0,esk4_0) = empty_set )
& ( ~ subset(esk3_0,esk4_0)
| set_difference(esk3_0,esk4_0) != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_18,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( subset(esk3_0,esk4_0)
| set_difference(esk3_0,esk4_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
~ in(X1,empty_set),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_13]) ).
cnf(c_0_22,plain,
( X3 = set_difference(X1,X2)
| in(esk2_3(X1,X2,X3),X3)
| in(esk2_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_23,plain,
! [X33,X34] :
( ~ empty(X34)
| ~ in(X33,X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
cnf(c_0_24,plain,
( X4 != set_difference(X2,X3)
| ~ in(X1,X2)
| in(X1,X4)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
( ~ in(X1,esk3_0)
| in(X1,esk4_0)
| set_difference(esk3_0,esk4_0) = empty_set ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_26,plain,
( in(esk2_3(X1,X2,empty_set),X1)
| set_difference(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( ~ empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( ~ in(esk2_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_30,negated_conjecture,
( in(esk2_3(esk3_0,X1,empty_set),esk4_0)
| set_difference(esk3_0,X1) = empty_set
| set_difference(esk3_0,esk4_0) = empty_set ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( ~ in(X1,X3)
| ~ empty(set_difference(X3,X2))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
set_difference(esk3_0,esk4_0) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_21]) ).
cnf(c_0_33,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_34,plain,
( ~ in(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_35,negated_conjecture,
( ~ in(X1,esk3_0)
| in(X1,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
( ~ subset(esk3_0,esk4_0)
| set_difference(esk3_0,esk4_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_37,negated_conjecture,
( ~ in(esk1_2(X1,esk4_0),esk3_0)
| subset(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
~ subset(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_32])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_14]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:51:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.43 % Version: 3.5.1
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2692672 completed with status 0
% 0.10/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.43 % No SInE strategy applied
% 0.10/0.43 % Search class: FGHSS-FFMS32-SFFFFFNN
% 0.10/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 191s (1) cores
% 0.10/0.43 % Starting new_bool_3 with 191s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 191s (1) cores
% 0.10/0.43 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 2692679 completed with status 0
% 0.10/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.43 % No SInE strategy applied
% 0.10/0.43 % Search class: FGHSS-FFMS32-SFFFFFNN
% 0.10/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 191s (1) cores
% 0.10/0.43 % Preprocessing time : 0.001 s
% 0.10/0.43 % Presaturation interreduction done
% 0.10/0.43
% 0.10/0.43 % Proof found!
% 0.10/0.43 % SZS status Theorem
% 0.10/0.43 % SZS output start CNFRefutation
% See solution above
% 0.10/0.43 % Parsed axioms : 16
% 0.10/0.43 % Removed by relevancy pruning/SinE : 0
% 0.10/0.43 % Initial clauses : 25
% 0.10/0.43 % Removed in clause preprocessing : 2
% 0.10/0.43 % Initial clauses in saturation : 23
% 0.10/0.43 % Processed clauses : 145
% 0.10/0.43 % ...of these trivial : 0
% 0.10/0.43 % ...subsumed : 40
% 0.10/0.43 % ...remaining for further processing : 105
% 0.10/0.43 % Other redundant clauses eliminated : 3
% 0.10/0.43 % Clauses deleted for lack of memory : 0
% 0.10/0.43 % Backward-subsumed : 1
% 0.10/0.43 % Backward-rewritten : 20
% 0.10/0.43 % Generated clauses : 236
% 0.10/0.43 % ...of the previous two non-redundant : 197
% 0.10/0.43 % ...aggressively subsumed : 0
% 0.10/0.43 % Contextual simplify-reflections : 1
% 0.10/0.43 % Paramodulations : 229
% 0.10/0.43 % Factorizations : 4
% 0.10/0.43 % NegExts : 0
% 0.10/0.43 % Equation resolutions : 3
% 0.10/0.43 % Disequality decompositions : 0
% 0.10/0.43 % Total rewrite steps : 56
% 0.10/0.43 % ...of those cached : 41
% 0.10/0.43 % Propositional unsat checks : 0
% 0.10/0.43 % Propositional check models : 0
% 0.10/0.43 % Propositional check unsatisfiable : 0
% 0.10/0.43 % Propositional clauses : 0
% 0.10/0.43 % Propositional clauses after purity: 0
% 0.10/0.43 % Propositional unsat core size : 0
% 0.10/0.43 % Propositional preprocessing time : 0.000
% 0.10/0.43 % Propositional encoding time : 0.000
% 0.10/0.43 % Propositional solver time : 0.000
% 0.10/0.43 % Success case prop preproc time : 0.000
% 0.10/0.43 % Success case prop encoding time : 0.000
% 0.10/0.43 % Success case prop solver time : 0.000
% 0.10/0.43 % Current number of processed clauses : 58
% 0.10/0.43 % Positive orientable unit clauses : 9
% 0.10/0.43 % Positive unorientable unit clauses: 0
% 0.10/0.43 % Negative unit clauses : 5
% 0.10/0.43 % Non-unit-clauses : 44
% 0.10/0.43 % Current number of unprocessed clauses: 95
% 0.10/0.43 % ...number of literals in the above : 283
% 0.10/0.43 % Current number of archived formulas : 0
% 0.10/0.43 % Current number of archived clauses : 44
% 0.10/0.43 % Clause-clause subsumption calls (NU) : 639
% 0.10/0.43 % Rec. Clause-clause subsumption calls : 458
% 0.10/0.43 % Non-unit clause-clause subsumptions : 24
% 0.10/0.43 % Unit Clause-clause subsumption calls : 63
% 0.10/0.43 % Rewrite failures with RHS unbound : 0
% 0.10/0.43 % BW rewrite match attempts : 17
% 0.10/0.43 % BW rewrite match successes : 5
% 0.10/0.43 % Condensation attempts : 0
% 0.10/0.43 % Condensation successes : 0
% 0.10/0.43 % Termbank termtop insertions : 4135
% 0.10/0.43 % Search garbage collected termcells : 393
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.008 s
% 0.10/0.43 % System time : 0.004 s
% 0.10/0.43 % Total time : 0.012 s
% 0.10/0.43 % Maximum resident set size: 3640 pages
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.027 s
% 0.10/0.43 % System time : 0.013 s
% 0.10/0.43 % Total time : 0.040 s
% 0.10/0.43 % Maximum resident set size: 4864 pages
% 0.10/0.43 % E exiting
%------------------------------------------------------------------------------