%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 02:13:01 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.62s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of clauses : 62 ( 17 unt; 13 nHn; 60 RR)
% Number of literals : 146 ( 0 equ; 75 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 108 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(member_of_difference,axiom,
( ~ member(X4,X3)
| ~ difference(X1,X2,X3)
| member(X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',member_of_difference) ).
cnf(prove_cDa_union_cDb_is_cD_aIb,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
cnf(member_of_difference_or_set2,axiom,
( ~ difference(X2,X3,X4)
| ~ member(X1,X2)
| member(X1,X3)
| member(X1,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',member_of_difference_or_set2) ).
cnf(c_minus_aIb,hypothesis,
difference(c,aIb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_aIb) ).
cnf(union_axiom1,axiom,
( member(g(X1,X2,X3),X3)
| member(g(X1,X2,X3),X2)
| member(g(X1,X2,X3),X1)
| union(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom1) ).
cnf(c_minus_b,hypothesis,
difference(c,b,cDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_b) ).
cnf(c_minus_a,hypothesis,
difference(c,a,cDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_a) ).
cnf(union_axiom3,axiom,
( ~ member(g(X1,X2,X3),X3)
| ~ member(g(X1,X2,X3),X2)
| union(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom3) ).
cnf(member_of_intersection_is_member_of_set2,axiom,
( ~ member(X4,X3)
| ~ intersection(X1,X2,X3)
| member(X4,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set2) ).
cnf(union_axiom2,axiom,
( ~ member(g(X1,X2,X3),X3)
| ~ member(g(X1,X2,X3),X1)
| union(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom2) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( ~ member(X4,X3)
| ~ intersection(X1,X2,X3)
| member(X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set1) ).
cnf(member_of_both_is_member_of_intersection,axiom,
( ~ member(X4,X1)
| ~ member(X4,X2)
| ~ intersection(X1,X2,X3)
| member(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_both_is_member_of_intersection) ).
cnf(a_intersection_b,hypothesis,
intersection(a,b,aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_b) ).
cnf(not_member_of_difference,axiom,
( ~ difference(X4,X2,X3)
| ~ member(X1,X3)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',not_member_of_difference) ).
cnf(c_0_14,plain,
( ~ member(X4,X3)
| ~ difference(X1,X2,X3)
| member(X4,X1) ),
inference(fof_simplification,[status(thm)],[member_of_difference]) ).
cnf(c_0_15,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
inference(fof_simplification,[status(thm)],[prove_cDa_union_cDb_is_cD_aIb]) ).
cnf(c_0_16,plain,
( ~ difference(X2,X3,X4)
| ~ member(X1,X2)
| member(X1,X3)
| member(X1,X4) ),
inference(fof_simplification,[status(thm)],[member_of_difference_or_set2]) ).
cnf(c_0_17,plain,
( ~ member(X4,X3)
| ~ difference(X1,X2,X3)
| member(X4,X1) ),
c_0_14 ).
cnf(c_0_18,hypothesis,
difference(c,aIb,cD_aIb),
c_minus_aIb ).
cnf(c_0_19,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
c_0_15 ).
cnf(c_0_20,axiom,
( member(g(X1,X2,X3),X3)
| member(g(X1,X2,X3),X2)
| member(g(X1,X2,X3),X1)
| union(X1,X2,X3) ),
union_axiom1 ).
cnf(c_0_21,hypothesis,
difference(c,b,cDb),
c_minus_b ).
cnf(c_0_22,hypothesis,
difference(c,a,cDa),
c_minus_a ).
cnf(c_0_23,plain,
( ~ difference(X2,X3,X4)
| ~ member(X1,X2)
| member(X1,X3)
| member(X1,X4) ),
c_0_16 ).
cnf(c_0_24,hypothesis,
( ~ member(X1,cD_aIb)
| member(X1,c) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,hypothesis,
( ~ member(X1,cDb)
| member(X1,c) ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_27,hypothesis,
( ~ member(X1,cDa)
| member(X1,c) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_28,plain,
( ~ member(g(X1,X2,X3),X3)
| ~ member(g(X1,X2,X3),X2)
| union(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[union_axiom3]) ).
cnf(c_0_29,hypothesis,
( ~ member(X1,c)
| member(X1,cD_aIb)
| member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_30,hypothesis,
member(g(cDa,cDb,cD_aIb),c),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]) ).
cnf(c_0_31,plain,
( ~ member(X4,X3)
| ~ intersection(X1,X2,X3)
| member(X4,X2) ),
inference(fof_simplification,[status(thm)],[member_of_intersection_is_member_of_set2]) ).
cnf(c_0_32,plain,
( ~ member(g(X1,X2,X3),X3)
| ~ member(g(X1,X2,X3),X1)
| union(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[union_axiom2]) ).
cnf(c_0_33,plain,
( ~ member(X4,X3)
| ~ intersection(X1,X2,X3)
| member(X4,X1) ),
inference(fof_simplification,[status(thm)],[member_of_intersection_is_member_of_set1]) ).
cnf(c_0_34,plain,
( ~ member(X4,X1)
| ~ member(X4,X2)
| ~ intersection(X1,X2,X3)
| member(X4,X3) ),
inference(fof_simplification,[status(thm)],[member_of_both_is_member_of_intersection]) ).
cnf(c_0_35,plain,
( ~ member(g(X1,X2,X3),X3)
| ~ member(g(X1,X2,X3),X2)
| union(X1,X2,X3) ),
c_0_28 ).
cnf(c_0_36,hypothesis,
( member(g(cDa,cDb,cD_aIb),aIb)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,hypothesis,
( ~ member(X1,c)
| member(X1,cDb)
| member(X1,b) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_38,plain,
( ~ member(X4,X3)
| ~ intersection(X1,X2,X3)
| member(X4,X2) ),
c_0_31 ).
cnf(c_0_39,hypothesis,
intersection(a,b,aIb),
a_intersection_b ).
cnf(c_0_40,plain,
( ~ member(g(X1,X2,X3),X3)
| ~ member(g(X1,X2,X3),X1)
| union(X1,X2,X3) ),
c_0_32 ).
cnf(c_0_41,hypothesis,
( ~ member(X1,c)
| member(X1,cDa)
| member(X1,a) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_42,plain,
( ~ member(X4,X3)
| ~ intersection(X1,X2,X3)
| member(X4,X1) ),
c_0_33 ).
cnf(c_0_43,plain,
( ~ difference(X4,X2,X3)
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_member_of_difference]) ).
cnf(c_0_44,plain,
( ~ member(X4,X1)
| ~ member(X4,X2)
| ~ intersection(X1,X2,X3)
| member(X4,X3) ),
c_0_34 ).
cnf(c_0_45,hypothesis,
( ~ member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),aIb) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19]) ).
cnf(c_0_46,hypothesis,
( member(g(cDa,cDb,cD_aIb),b)
| member(g(cDa,cDb,cD_aIb),cDb) ),
inference(spm,[status(thm)],[c_0_37,c_0_30]) ).
cnf(c_0_47,hypothesis,
( ~ member(X1,aIb)
| member(X1,b) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,hypothesis,
( ~ member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),aIb) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_19]) ).
cnf(c_0_49,hypothesis,
( member(g(cDa,cDb,cD_aIb),a)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(spm,[status(thm)],[c_0_41,c_0_30]) ).
cnf(c_0_50,hypothesis,
( ~ member(X1,aIb)
| member(X1,a) ),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_51,plain,
( ~ difference(X4,X2,X3)
| ~ member(X1,X3)
| ~ member(X1,X2) ),
c_0_43 ).
cnf(c_0_52,hypothesis,
( ~ member(X1,a)
| ~ member(X1,b)
| member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_44,c_0_39]) ).
cnf(c_0_53,hypothesis,
member(g(cDa,cDb,cD_aIb),b),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_54,hypothesis,
member(g(cDa,cDb,cD_aIb),a),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_55,hypothesis,
( ~ member(X1,aIb)
| ~ member(X1,cD_aIb) ),
inference(spm,[status(thm)],[c_0_51,c_0_18]) ).
cnf(c_0_56,hypothesis,
member(g(cDa,cDb,cD_aIb),aIb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).
cnf(c_0_57,hypothesis,
( ~ member(X1,b)
| ~ member(X1,cDb) ),
inference(spm,[status(thm)],[c_0_51,c_0_21]) ).
cnf(c_0_58,hypothesis,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cDb) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_25]),c_0_56])]) ).
cnf(c_0_59,hypothesis,
( ~ member(X1,a)
| ~ member(X1,cDa) ),
inference(spm,[status(thm)],[c_0_51,c_0_22]) ).
cnf(c_0_60,hypothesis,
member(g(cDa,cDb,cD_aIb),cDa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_53])]) ).
cnf(c_0_61,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.52 % Computer : n026.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Mon Sep 21 04:44:37 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.57 Running first-order theorem proving
% 0.09/0.57 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
% 0.16/0.62 % Version: 3.5.1
% 0.16/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.62 % Starting sh5l with 300s (1) cores
% 0.16/0.62 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1391844 completed with status 0
% 0.16/0.62 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.62 % No SInE strategy applied
% 0.16/0.62 % Search class: FGHNF-FFMS32-SFFFFFNN
% 0.16/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.62 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.16/0.62 % Starting G-E--_107_C12_11_nc_F1_PI_AE_Q4_CS_SP_PS_S071I with 136s (1) cores
% 0.16/0.62 % Starting new_bool_3 with 136s (1) cores
% 0.16/0.62 % G-E--_107_C12_11_nc_F1_PI_AE_Q4_CS_SP_PS_S071I with pid 1391854 completed with status 0
% 0.16/0.62 % Result found by G-E--_107_C12_11_nc_F1_PI_AE_Q4_CS_SP_PS_S071I
% 0.16/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.62 % No SInE strategy applied
% 0.16/0.62 % Search class: FGHNF-FFMS32-SFFFFFNN
% 0.16/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.62 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.16/0.62 % Starting G-E--_107_C12_11_nc_F1_PI_AE_Q4_CS_SP_PS_S071I with 136s (1) cores
% 0.16/0.62 % Preprocessing time : 0.002 s
% 0.16/0.62 % Presaturation interreduction done
% 0.16/0.62
% 0.16/0.62 % Proof found!
% 0.16/0.62 % SZS status Unsatisfiable
% 0.16/0.62 % SZS output start CNFRefutation
% See solution above
% 0.16/0.62 % Parsed axioms : 29
% 0.16/0.62 % Removed by relevancy pruning/SinE : 0
% 0.16/0.62 % Initial clauses : 29
% 0.16/0.62 % Removed in clause preprocessing : 0
% 0.16/0.62 % Initial clauses in saturation : 29
% 0.16/0.62 % Processed clauses : 199
% 0.16/0.62 % ...of these trivial : 10
% 0.16/0.62 % ...subsumed : 0
% 0.16/0.62 % ...remaining for further processing : 189
% 0.16/0.62 % Other redundant clauses eliminated : 0
% 0.16/0.62 % Clauses deleted for lack of memory : 0
% 0.16/0.62 % Backward-subsumed : 3
% 0.16/0.62 % Backward-rewritten : 22
% 0.16/0.62 % Generated clauses : 1153
% 0.16/0.62 % ...of the previous two non-redundant : 933
% 0.16/0.62 % ...aggressively subsumed : 0
% 0.16/0.62 % Contextual simplify-reflections : 4
% 0.16/0.62 % Paramodulations : 1153
% 0.16/0.62 % Factorizations : 0
% 0.16/0.62 % NegExts : 0
% 0.16/0.62 % Equation resolutions : 0
% 0.16/0.62 % Disequality decompositions : 0
% 0.16/0.62 % Total rewrite steps : 309
% 0.16/0.62 % ...of those cached : 281
% 0.16/0.62 % Propositional unsat checks : 0
% 0.16/0.62 % Propositional check models : 0
% 0.16/0.62 % Propositional check unsatisfiable : 0
% 0.16/0.62 % Propositional clauses : 0
% 0.16/0.62 % Propositional clauses after purity: 0
% 0.16/0.62 % Propositional unsat core size : 0
% 0.16/0.62 % Propositional preprocessing time : 0.000
% 0.16/0.62 % Propositional encoding time : 0.000
% 0.16/0.62 % Propositional solver time : 0.000
% 0.16/0.62 % Success case prop preproc time : 0.000
% 0.16/0.62 % Success case prop encoding time : 0.000
% 0.16/0.62 % Success case prop solver time : 0.000
% 0.16/0.62 % Current number of processed clauses : 135
% 0.16/0.62 % Positive orientable unit clauses : 32
% 0.16/0.62 % Positive unorientable unit clauses: 0
% 0.16/0.62 % Negative unit clauses : 1
% 0.16/0.62 % Non-unit-clauses : 102
% 0.16/0.62 % Current number of unprocessed clauses: 763
% 0.16/0.62 % ...number of literals in the above : 3031
% 0.16/0.62 % Current number of archived formulas : 0
% 0.16/0.62 % Current number of archived clauses : 54
% 0.16/0.62 % Clause-clause subsumption calls (NU) : 3503
% 0.16/0.62 % Rec. Clause-clause subsumption calls : 2081
% 0.16/0.62 % Non-unit clause-clause subsumptions : 6
% 0.16/0.62 % Unit Clause-clause subsumption calls : 909
% 0.16/0.62 % Rewrite failures with RHS unbound : 0
% 0.16/0.62 % BW rewrite match attempts : 9
% 0.16/0.62 % BW rewrite match successes : 9
% 0.16/0.62 % Condensation attempts : 0
% 0.16/0.62 % Condensation successes : 0
% 0.16/0.62 % Termbank termtop insertions : 20224
% 0.16/0.62 % Search garbage collected termcells : 67
% 0.16/0.62
% 0.16/0.62 % -------------------------------------------------
% 0.16/0.62 % User time : 0.026 s
% 0.16/0.62 % System time : 0.003 s
% 0.16/0.62 % Total time : 0.030 s
% 0.16/0.62 % Maximum resident set size: 3656 pages
% 0.16/0.62
% 0.16/0.62 % -------------------------------------------------
% 0.16/0.62 % User time : 0.120 s
% 0.16/0.62 % System time : 0.017 s
% 0.16/0.62 % Total time : 0.137 s
% 0.16/0.62 % Maximum resident set size: 4864 pages
% 0.16/0.62 % E exiting
%------------------------------------------------------------------------------