%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 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 : Thu Sep 24 02:15:44 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 39 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 34 ( 14 ~; 9 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t53_zfmisc_1,conjecture,
! [X1,X2,X3] :
( ( in(X3,X2)
& in(X1,X2) )
=> set_intersection2(unordered_pair(X1,X3),X2) = unordered_pair(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t28_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(t38_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X2,X3)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( ( in(X3,X2)
& in(X1,X2) )
=> set_intersection2(unordered_pair(X1,X3),X2) = unordered_pair(X1,X3) ),
inference(assume_negation,[status(cth)],[t53_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
( set_intersection2(unordered_pair(esk1_0,esk3_0),esk2_0) != unordered_pair(esk1_0,esk3_0)
& in(esk3_0,esk2_0)
& in(esk1_0,esk2_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,
! [X12,X13] : set_intersection2(X12,X13) = set_intersection2(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_7,plain,
! [X15,X16] :
( set_intersection2(X15,X16) = X15
| ~ subset(X15,X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])])]) ).
cnf(c_0_8,negated_conjecture,
set_intersection2(unordered_pair(esk1_0,esk3_0),esk2_0) != unordered_pair(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ subset(X1,X2)
| set_intersection2(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0)) != unordered_pair(esk1_0,esk3_0),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( ~ subset(X2,X1)
| set_intersection2(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_13,plain,
! [X9,X10,X11] :
( ( subset(unordered_pair(X9,X10),X11)
| ~ in(X10,X11)
| ~ in(X9,X11) )
& ( ~ subset(unordered_pair(X9,X10),X11)
| in(X10,X11) )
& ( ~ subset(unordered_pair(X9,X10),X11)
| in(X9,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])])]) ).
cnf(c_0_14,negated_conjecture,
~ subset(unordered_pair(esk1_0,esk3_0),esk2_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( ~ in(X3,X2)
| ~ in(X1,X2)
| subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
in(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
in(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 05:43:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.44 % Version: 3.5.1
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % sh5l with pid 53143 completed with status 0
% 0.11/0.44 % Result found by sh5l
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.44 % Search class: FHHSM-FFSF22-SFFFFFNN
% 0.11/0.44 % partial match(1): FHUSM-FFSF22-SFFFFFNN
% 0.11/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % SubtermCWHack with pid 53144 completed with status 0
% 0.11/0.44 % Result found by SubtermCWHack
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.44 % Search class: FHHSM-FFSF22-SFFFFFNN
% 0.11/0.44 % partial match(1): FHUSM-FFSF22-SFFFFFNN
% 0.11/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % Preprocessing time : 0.001 s
% 0.11/0.44
% 0.11/0.44 % Proof found!
% 0.11/0.44 % SZS status Theorem
% 0.11/0.44 % SZS output start CNFRefutation
% See solution above
% 0.11/0.44 % Parsed axioms : 10
% 0.11/0.44 % Removed by relevancy pruning/SinE : 2
% 0.11/0.44 % Initial clauses : 12
% 0.11/0.44 % Removed in clause preprocessing : 0
% 0.11/0.44 % Initial clauses in saturation : 12
% 0.11/0.44 % Processed clauses : 33
% 0.11/0.44 % ...of these trivial : 1
% 0.11/0.44 % ...subsumed : 11
% 0.11/0.44 % ...remaining for further processing : 21
% 0.11/0.44 % Other redundant clauses eliminated : 0
% 0.11/0.44 % Clauses deleted for lack of memory : 0
% 0.11/0.44 % Backward-subsumed : 0
% 0.11/0.44 % Backward-rewritten : 0
% 0.11/0.44 % Generated clauses : 33
% 0.11/0.44 % ...of the previous two non-redundant : 23
% 0.11/0.44 % ...aggressively subsumed : 0
% 0.11/0.44 % Contextual simplify-reflections : 0
% 0.11/0.44 % Paramodulations : 33
% 0.11/0.44 % Factorizations : 0
% 0.11/0.44 % NegExts : 0
% 0.11/0.44 % Equation resolutions : 0
% 0.11/0.44 % Disequality decompositions : 0
% 0.11/0.44 % Total rewrite steps : 9
% 0.11/0.44 % ...of those cached : 3
% 0.11/0.44 % Propositional unsat checks : 0
% 0.11/0.44 % Propositional check models : 0
% 0.11/0.44 % Propositional check unsatisfiable : 0
% 0.11/0.44 % Propositional clauses : 0
% 0.11/0.44 % Propositional clauses after purity: 0
% 0.11/0.44 % Propositional unsat core size : 0
% 0.11/0.44 % Propositional preprocessing time : 0.000
% 0.11/0.44 % Propositional encoding time : 0.000
% 0.11/0.44 % Propositional solver time : 0.000
% 0.11/0.44 % Success case prop preproc time : 0.000
% 0.11/0.44 % Success case prop encoding time : 0.000
% 0.11/0.44 % Success case prop solver time : 0.000
% 0.11/0.44 % Current number of processed clauses : 21
% 0.11/0.44 % Positive orientable unit clauses : 6
% 0.11/0.44 % Positive unorientable unit clauses: 2
% 0.11/0.44 % Negative unit clauses : 6
% 0.11/0.44 % Non-unit-clauses : 7
% 0.11/0.44 % Current number of unprocessed clauses: 1
% 0.11/0.44 % ...number of literals in the above : 2
% 0.11/0.44 % Current number of archived formulas : 0
% 0.11/0.44 % Current number of archived clauses : 0
% 0.11/0.44 % Clause-clause subsumption calls (NU) : 17
% 0.11/0.44 % Rec. Clause-clause subsumption calls : 17
% 0.11/0.44 % Non-unit clause-clause subsumptions : 7
% 0.11/0.44 % Unit Clause-clause subsumption calls : 1
% 0.11/0.44 % Rewrite failures with RHS unbound : 0
% 0.11/0.44 % BW rewrite match attempts : 3
% 0.11/0.44 % BW rewrite match successes : 2
% 0.11/0.44 % Condensation attempts : 0
% 0.11/0.44 % Condensation successes : 0
% 0.11/0.44 % Termbank termtop insertions : 766
% 0.11/0.44 % Search garbage collected termcells : 109
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.002 s
% 0.11/0.44 % System time : 0.003 s
% 0.11/0.44 % Total time : 0.005 s
% 0.11/0.44 % Maximum resident set size: 3636 pages
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.004 s
% 0.11/0.44 % System time : 0.008 s
% 0.11/0.44 % Total time : 0.011 s
% 0.11/0.44 % Maximum resident set size: 4864 pages
% 0.11/0.44 % E exiting
%------------------------------------------------------------------------------