%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% 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 02:15:23 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 33 ( 14 unt; 7 nHn; 24 RR)
% Number of literals : 55 ( 7 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause120,axiom,
( ~ member(X1,union(X2))
| member(unionE_sk1(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
cnf(clause112,axiom,
( ~ member(X1,cons(X2,X3))
| member(X1,X3)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
cnf(un_eq_Union_2_c1,negated_conjecture,
member(sk2,union(cons(a,cons(b,eptset)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c1) ).
cnf(clause119,axiom,
( ~ member(X1,union(X2))
| member(X1,unionE_sk1(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
cnf(clause158,axiom,
~ member(X1,eptset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause158) ).
cnf(unI1,axiom,
( ~ member(X1,X2)
| member(X1,un(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI1) ).
cnf(un_eq_Union_2_c2,negated_conjecture,
~ member(sk2,un(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c2) ).
cnf(unI2,axiom,
( ~ member(X1,X2)
| member(X1,un(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI2) ).
cnf(c_0_8,plain,
( ~ member(X1,union(X2))
| member(unionE_sk1(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_9,plain,
( ~ member(X1,cons(X2,X3))
| member(X1,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[clause112]) ).
cnf(c_0_10,plain,
( ~ member(X1,union(X2))
| member(unionE_sk1(X1,X2),X2) ),
c_0_8 ).
cnf(c_0_11,negated_conjecture,
member(sk2,union(cons(a,cons(b,eptset)))),
un_eq_Union_2_c1 ).
cnf(c_0_12,plain,
( ~ member(X1,union(X2))
| member(X1,unionE_sk1(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause119]) ).
cnf(c_0_13,plain,
( ~ member(X1,cons(X2,X3))
| member(X1,X3)
| X1 = X2 ),
c_0_9 ).
cnf(c_0_14,negated_conjecture,
member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
~ member(X1,eptset),
inference(fof_simplification,[status(thm)],[clause158]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| member(X1,un(X2,X3)) ),
inference(fof_simplification,[status(thm)],[unI1]) ).
cnf(c_0_17,plain,
( ~ member(X1,union(X2))
| member(X1,unionE_sk1(X1,X2)) ),
c_0_12 ).
cnf(c_0_18,negated_conjecture,
( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
~ member(X1,eptset),
c_0_15 ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| member(X1,un(X2,X3)) ),
c_0_16 ).
cnf(c_0_21,negated_conjecture,
member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))),
inference(spm,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_22,negated_conjecture,
( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
~ member(sk2,un(a,b)),
inference(fof_simplification,[status(thm)],[un_eq_Union_2_c2]) ).
cnf(c_0_24,negated_conjecture,
member(sk2,un(unionE_sk1(sk2,cons(a,cons(b,eptset))),X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( member(sk2,b)
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ member(X1,X2)
| member(X1,un(X3,X2)) ),
inference(fof_simplification,[status(thm)],[unI2]) ).
cnf(c_0_27,negated_conjecture,
~ member(sk2,un(a,b)),
c_0_23 ).
cnf(c_0_28,negated_conjecture,
( member(sk2,b)
| member(sk2,un(a,X1)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( ~ member(X1,X2)
| member(X1,un(X3,X2)) ),
c_0_26 ).
cnf(c_0_30,negated_conjecture,
member(sk2,b),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
member(sk2,un(X1,b)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.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 05:42:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.45 % Version: 3.5.1
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1674722 completed with status 0
% 0.10/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.45 % No SInE strategy applied
% 0.10/0.45 % Search class: FGUSF-FFSF21-MFFFFFNN
% 0.10/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.10/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.45 % new_bool_1 with pid 1674731 completed with status 0
% 0.10/0.45 % Result found by new_bool_1
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.45 % No SInE strategy applied
% 0.10/0.45 % Search class: FGUSF-FFSF21-MFFFFFNN
% 0.10/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.10/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.45 % Preprocessing time : 0.001 s
% 0.10/0.45 % Presaturation interreduction done
% 0.10/0.45
% 0.10/0.45 % Proof found!
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 14
% 0.10/0.45 % Removed by relevancy pruning/SinE : 0
% 0.10/0.45 % Initial clauses : 14
% 0.10/0.45 % Removed in clause preprocessing : 0
% 0.10/0.45 % Initial clauses in saturation : 14
% 0.10/0.45 % Processed clauses : 66
% 0.10/0.45 % ...of these trivial : 0
% 0.10/0.45 % ...subsumed : 0
% 0.10/0.45 % ...remaining for further processing : 66
% 0.10/0.45 % Other redundant clauses eliminated : 0
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 1
% 0.10/0.45 % Backward-rewritten : 4
% 0.10/0.45 % Generated clauses : 126
% 0.10/0.45 % ...of the previous two non-redundant : 121
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 0
% 0.10/0.45 % Paramodulations : 125
% 0.10/0.45 % Factorizations : 1
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 0
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 6
% 0.10/0.45 % ...of those cached : 3
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 47
% 0.10/0.45 % Positive orientable unit clauses : 21
% 0.10/0.45 % Positive unorientable unit clauses: 0
% 0.10/0.45 % Negative unit clauses : 1
% 0.10/0.45 % Non-unit-clauses : 25
% 0.10/0.45 % Current number of unprocessed clauses: 83
% 0.10/0.45 % ...number of literals in the above : 151
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 19
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 70
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 67
% 0.10/0.45 % Non-unit clause-clause subsumptions : 0
% 0.10/0.45 % Unit Clause-clause subsumption calls : 8
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 8
% 0.10/0.45 % BW rewrite match successes : 2
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 2292
% 0.10/0.45 % Search garbage collected termcells : 28
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.005 s
% 0.10/0.45 % System time : 0.004 s
% 0.10/0.45 % Total time : 0.010 s
% 0.10/0.45 % Maximum resident set size: 3384 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.039 s
% 0.10/0.45 % System time : 0.020 s
% 0.10/0.45 % Total time : 0.059 s
% 0.10/0.45 % Maximum resident set size: 4608 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------