%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET874+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:15:40 PM UTC 2026
% Result : Theorem 0.25s 0.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 49 ( 34 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 47 ( 19 ~; 20 |; 5 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 44 ( 3 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t14_zfmisc_1,conjecture,
! [X1,X2] : set_union2(singleton(X1),unordered_pair(X1,X2)) = unordered_pair(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_zfmisc_1) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(l23_zfmisc_1,axiom,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] : set_union2(singleton(X1),unordered_pair(X1,X2)) = unordered_pair(X1,X2),
inference(assume_negation,[status(cth)],[t14_zfmisc_1]) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14,X15,X16,X17,X18] :
( ( X18 = unordered_pair(X16,X17)
| esk1_3(X16,X17,X18) = X17
| esk1_3(X16,X17,X18) = X16
| in(esk1_3(X16,X17,X18),X18) )
& ( X18 = unordered_pair(X16,X17)
| ~ in(esk1_3(X16,X17,X18),X18)
| esk1_3(X16,X17,X18) != X17 )
& ( X18 = unordered_pair(X16,X17)
| ~ in(esk1_3(X16,X17,X18),X18)
| esk1_3(X16,X17,X18) != X16 )
& ( X13 != unordered_pair(X11,X12)
| in(X15,X13)
| X15 != X12 )
& ( X13 != unordered_pair(X11,X12)
| in(X15,X13)
| X15 != X11 )
& ( X13 != unordered_pair(X11,X12)
| X14 = X12
| X14 = X11
| ~ in(X14,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)],[d2_tarski])])])])])])]) ).
fof(c_0_7,negated_conjecture,
set_union2(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != unordered_pair(esk4_0,esk5_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,plain,
! [X9,X10] : set_union2(X9,X10) = set_union2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_9,plain,
! [X25,X26] :
( set_union2(singleton(X25),X26) = X26
| ~ in(X25,X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])])]) ).
cnf(c_0_10,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,negated_conjecture,
set_union2(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != unordered_pair(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ in(X1,X2)
| set_union2(singleton(X1),X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).
cnf(c_0_16,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
set_union2(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)) != unordered_pair(esk4_0,esk5_0),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( ~ in(X2,X1)
| set_union2(X1,singleton(X2)) = X1 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET874+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.46 % Computer : n016.cluster.edu
% 0.22/0.46 % Model : x86_64 x86_64
% 0.22/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.46 % Memory : 8046.5625MB
% 0.22/0.46 % OS : Linux 6.8.0-71-generic
% 0.22/0.46 % CPULimit : 300
% 0.22/0.46 % WCLimit : 300
% 0.22/0.46 % DateTime : Mon Sep 21 05:47:22 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.56 Running first-order theorem proving
% 0.25/0.56 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.25/0.61 % Version: 3.5.1
% 0.25/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.61 % Starting sh5l with 300s (1) cores
% 0.25/0.61 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1682628 completed with status 0
% 0.25/0.61 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.25/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.61 % No SInE strategy applied
% 0.25/0.61 % Search class: FGHSS-FFSF32-SFFFFFNN
% 0.25/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.25/0.61 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.61 % Starting new_bool_1 with 136s (1) cores
% 0.25/0.61 % SubtermCWHack with pid 1682632 completed with status 0
% 0.25/0.61 % Result found by SubtermCWHack
% 0.25/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.61 % No SInE strategy applied
% 0.25/0.61 % Search class: FGHSS-FFSF32-SFFFFFNN
% 0.25/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.61 % Preprocessing time : 0.001 s
% 0.25/0.61
% 0.25/0.61 % Proof found!
% 0.25/0.61 % SZS status Theorem
% 0.25/0.61 % SZS output start CNFRefutation
% See solution above
% 0.25/0.61 % Parsed axioms : 11
% 0.25/0.61 % Removed by relevancy pruning/SinE : 0
% 0.25/0.61 % Initial clauses : 16
% 0.25/0.61 % Removed in clause preprocessing : 0
% 0.25/0.61 % Initial clauses in saturation : 16
% 0.25/0.61 % Processed clauses : 38
% 0.25/0.61 % ...of these trivial : 1
% 0.25/0.61 % ...subsumed : 16
% 0.25/0.61 % ...remaining for further processing : 21
% 0.25/0.61 % Other redundant clauses eliminated : 5
% 0.25/0.61 % Clauses deleted for lack of memory : 0
% 0.25/0.61 % Backward-subsumed : 0
% 0.25/0.61 % Backward-rewritten : 0
% 0.25/0.61 % Generated clauses : 37
% 0.25/0.61 % ...of the previous two non-redundant : 27
% 0.25/0.61 % ...aggressively subsumed : 0
% 0.25/0.61 % Contextual simplify-reflections : 0
% 0.25/0.61 % Paramodulations : 34
% 0.25/0.61 % Factorizations : 0
% 0.25/0.61 % NegExts : 0
% 0.25/0.61 % Equation resolutions : 5
% 0.25/0.61 % Disequality decompositions : 0
% 0.25/0.61 % Total rewrite steps : 8
% 0.25/0.61 % ...of those cached : 3
% 0.25/0.61 % Propositional unsat checks : 0
% 0.25/0.61 % Propositional check models : 0
% 0.25/0.61 % Propositional check unsatisfiable : 0
% 0.25/0.61 % Propositional clauses : 0
% 0.25/0.61 % Propositional clauses after purity: 0
% 0.25/0.61 % Propositional unsat core size : 0
% 0.25/0.61 % Propositional preprocessing time : 0.000
% 0.25/0.61 % Propositional encoding time : 0.000
% 0.25/0.61 % Propositional solver time : 0.000
% 0.25/0.61 % Success case prop preproc time : 0.000
% 0.25/0.61 % Success case prop encoding time : 0.000
% 0.25/0.61 % Success case prop solver time : 0.000
% 0.25/0.61 % Current number of processed clauses : 18
% 0.25/0.61 % Positive orientable unit clauses : 4
% 0.25/0.61 % Positive unorientable unit clauses: 2
% 0.25/0.61 % Negative unit clauses : 4
% 0.25/0.61 % Non-unit-clauses : 8
% 0.25/0.61 % Current number of unprocessed clauses: 5
% 0.25/0.61 % ...number of literals in the above : 16
% 0.25/0.61 % Current number of archived formulas : 0
% 0.25/0.61 % Current number of archived clauses : 0
% 0.25/0.61 % Clause-clause subsumption calls (NU) : 24
% 0.25/0.61 % Rec. Clause-clause subsumption calls : 24
% 0.25/0.61 % Non-unit clause-clause subsumptions : 12
% 0.25/0.61 % Unit Clause-clause subsumption calls : 1
% 0.25/0.61 % Rewrite failures with RHS unbound : 0
% 0.25/0.61 % BW rewrite match attempts : 7
% 0.25/0.61 % BW rewrite match successes : 6
% 0.25/0.61 % Condensation attempts : 0
% 0.25/0.61 % Condensation successes : 0
% 0.25/0.61 % Termbank termtop insertions : 1101
% 0.25/0.61 % Search garbage collected termcells : 223
% 0.25/0.62
% 0.25/0.62 % -------------------------------------------------
% 0.25/0.62 % User time : 0.005 s
% 0.25/0.62 % System time : 0.006 s
% 0.25/0.62 % Total time : 0.011 s
% 0.25/0.62 % Maximum resident set size: 3584 pages
% 0.25/0.62
% 0.25/0.62 % -------------------------------------------------
% 0.25/0.62 % User time : 0.015 s
% 0.25/0.62 % System time : 0.020 s
% 0.25/0.62 % Total time : 0.035 s
% 0.25/0.62 % Maximum resident set size: 4608 pages
% 0.25/0.62 % E exiting
%------------------------------------------------------------------------------