%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET011-1 : 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 : n008.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 0.14s 0.87s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 51 ( 10 unt; 19 nHn; 39 RR)
% Number of literals : 126 ( 0 equ; 60 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 94 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(a_minus_aDb,hypothesis,
difference(a,aDb,aD_aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_minus_aDb) ).
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(subsets_axiom1,axiom,
( member(member_of_1_not_of_2(X1,X2),X1)
| subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).
cnf(a_minus_b,hypothesis,
difference(a,b,aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_minus_b) ).
cnf(subsets_axiom2,axiom,
( ~ member(member_of_1_not_of_2(X1,X2),X2)
| subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).
cnf(membership_in_subsets,axiom,
( ~ subset(X2,X3)
| ~ member(X1,X2)
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',membership_in_subsets) ).
cnf(intersection_axiom3,axiom,
( ~ member(h(X1,X2,X3),X1)
| ~ member(h(X1,X2,X3),X2)
| ~ member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom3) ).
cnf(intersection_axiom2,axiom,
( member(h(X1,X2,X3),X2)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom2) ).
cnf(intersection_axiom1,axiom,
( member(h(X1,X2,X3),X1)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom1) ).
cnf(prove_a_intersection_b_is_aD_aDb,negated_conjecture,
~ intersection(a,b,aD_aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_intersection_b_is_aD_aDb) ).
cnf(c_0_12,plain,
( ~ difference(X4,X2,X3)
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_member_of_difference]) ).
cnf(c_0_13,plain,
( ~ member(X4,X3)
| ~ difference(X1,X2,X3)
| member(X4,X1) ),
inference(fof_simplification,[status(thm)],[member_of_difference]) ).
cnf(c_0_14,plain,
( ~ difference(X4,X2,X3)
| ~ member(X1,X3)
| ~ member(X1,X2) ),
c_0_12 ).
cnf(c_0_15,hypothesis,
difference(a,aDb,aD_aDb),
a_minus_aDb ).
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_13 ).
cnf(c_0_18,hypothesis,
( ~ member(X1,aDb)
| ~ member(X1,aD_aDb) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,axiom,
( member(member_of_1_not_of_2(X1,X2),X1)
| subset(X1,X2) ),
subsets_axiom1 ).
cnf(c_0_20,plain,
( ~ difference(X2,X3,X4)
| ~ member(X1,X2)
| member(X1,X3)
| member(X1,X4) ),
c_0_16 ).
cnf(c_0_21,hypothesis,
difference(a,b,aDb),
a_minus_b ).
cnf(c_0_22,hypothesis,
( ~ member(X1,aD_aDb)
| member(X1,a) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_23,plain,
( ~ member(member_of_1_not_of_2(X1,X2),X2)
| subset(X1,X2) ),
inference(fof_simplification,[status(thm)],[subsets_axiom2]) ).
cnf(c_0_24,hypothesis,
( ~ member(member_of_1_not_of_2(aD_aDb,X1),aDb)
| subset(aD_aDb,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,hypothesis,
( ~ member(X1,a)
| member(X1,b)
| member(X1,aDb) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,hypothesis,
( member(member_of_1_not_of_2(aD_aDb,X1),a)
| subset(aD_aDb,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_27,plain,
( ~ subset(X2,X3)
| ~ member(X1,X2)
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[membership_in_subsets]) ).
cnf(c_0_28,plain,
( ~ member(member_of_1_not_of_2(X1,X2),X2)
| subset(X1,X2) ),
c_0_23 ).
cnf(c_0_29,hypothesis,
( member(member_of_1_not_of_2(aD_aDb,X1),b)
| subset(aD_aDb,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
( ~ subset(X2,X3)
| ~ member(X1,X2)
| member(X1,X3) ),
c_0_27 ).
cnf(c_0_31,hypothesis,
subset(aD_aDb,b),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
( ~ member(h(X1,X2,X3),X1)
| ~ member(h(X1,X2,X3),X2)
| ~ member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[intersection_axiom3]) ).
cnf(c_0_33,hypothesis,
( ~ member(X1,aD_aDb)
| member(X1,b) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
( member(h(X1,X2,X3),X2)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X3) ),
intersection_axiom2 ).
cnf(c_0_35,plain,
( ~ member(h(X1,X2,X3),X1)
| ~ member(h(X1,X2,X3),X2)
| ~ member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3) ),
c_0_32 ).
cnf(c_0_36,hypothesis,
( ~ member(X1,a)
| member(X1,aDb)
| member(X1,aD_aDb) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_37,hypothesis,
( member(h(X1,X2,aD_aDb),X2)
| member(h(X1,X2,aD_aDb),b)
| intersection(X1,X2,aD_aDb) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,axiom,
( member(h(X1,X2,X3),X1)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X3) ),
intersection_axiom1 ).
cnf(c_0_39,hypothesis,
( ~ member(h(X1,X2,aD_aDb),X1)
| ~ member(h(X1,X2,aD_aDb),X2)
| ~ member(h(X1,X2,aD_aDb),a)
| member(h(X1,X2,aD_aDb),aDb)
| intersection(X1,X2,aD_aDb) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,hypothesis,
( member(h(X1,b,aD_aDb),b)
| intersection(X1,b,aD_aDb) ),
inference(ef,[status(thm)],[c_0_37]) ).
cnf(c_0_41,hypothesis,
( member(h(X1,X2,aD_aDb),X1)
| member(h(X1,X2,aD_aDb),a)
| intersection(X1,X2,aD_aDb) ),
inference(spm,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
~ intersection(a,b,aD_aDb),
inference(fof_simplification,[status(thm)],[prove_a_intersection_b_is_aD_aDb]) ).
cnf(c_0_43,hypothesis,
( ~ member(h(X1,b,aD_aDb),X1)
| ~ member(h(X1,b,aD_aDb),a)
| member(h(X1,b,aD_aDb),aDb)
| intersection(X1,b,aD_aDb) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,hypothesis,
( member(h(a,X1,aD_aDb),a)
| intersection(a,X1,aD_aDb) ),
inference(ef,[status(thm)],[c_0_41]) ).
cnf(c_0_45,negated_conjecture,
~ intersection(a,b,aD_aDb),
c_0_42 ).
cnf(c_0_46,hypothesis,
( ~ member(X1,b)
| ~ member(X1,aDb) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_47,hypothesis,
( ~ member(h(a,b,aD_aDb),a)
| member(h(a,b,aD_aDb),aDb) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_48,hypothesis,
( ~ member(h(a,b,aD_aDb),a)
| ~ member(h(a,b,aD_aDb),b) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,hypothesis,
~ member(h(a,b,aD_aDb),a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_40]),c_0_45]) ).
cnf(c_0_50,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.77 % Computer : n008.cluster.edu
% 0.10/0.77 % Model : x86_64 x86_64
% 0.10/0.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.77 % Memory : 8046.5625MB
% 0.10/0.77 % OS : Linux 6.8.0-71-generic
% 0.10/0.77 % CPULimit : 300
% 0.10/0.77 % WCLimit : 300
% 0.10/0.77 % DateTime : Mon Sep 21 04:42:25 UTC 2026
% 0.10/0.77 % CPUTime :
% 0.10/0.77 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.82 Running first-order theorem proving
% 0.14/0.82 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
% 0.14/0.87 % Version: 3.5.1
% 0.14/0.87 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.87 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.87 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.87 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.87 % Starting sh5l with 300s (1) cores
% 0.14/0.87 % sh5l with pid 161516 completed with status 0
% 0.14/0.87 % Result found by sh5l
% 0.14/0.87 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.87 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.87 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.87 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.87 % Starting sh5l with 300s (1) cores
% 0.14/0.87 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.87 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.87 % Search class: FGHNF-FFMF32-SFFFFFNN
% 0.14/0.87 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.87 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.87 % SubtermCWHack with pid 161518 completed with status 0
% 0.14/0.87 % Result found by SubtermCWHack
% 0.14/0.87 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.87 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.87 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.87 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.87 % Starting sh5l with 300s (1) cores
% 0.14/0.87 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.87 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.87 % Search class: FGHNF-FFMF32-SFFFFFNN
% 0.14/0.87 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.87 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.87 % Preprocessing time : 0.001 s
% 0.14/0.87
% 0.14/0.87 % Proof found!
% 0.14/0.87 % SZS status Unsatisfiable
% 0.14/0.87 % SZS output start CNFRefutation
% See solution above
% 0.14/0.87 % Parsed axioms : 21
% 0.14/0.87 % Removed by relevancy pruning/SinE : 0
% 0.14/0.87 % Initial clauses : 21
% 0.14/0.87 % Removed in clause preprocessing : 0
% 0.14/0.87 % Initial clauses in saturation : 21
% 0.14/0.87 % Processed clauses : 657
% 0.14/0.87 % ...of these trivial : 24
% 0.14/0.87 % ...subsumed : 429
% 0.14/0.87 % ...remaining for further processing : 204
% 0.14/0.87 % Other redundant clauses eliminated : 0
% 0.14/0.87 % Clauses deleted for lack of memory : 0
% 0.14/0.87 % Backward-subsumed : 8
% 0.14/0.87 % Backward-rewritten : 3
% 0.14/0.87 % Generated clauses : 843
% 0.14/0.87 % ...of the previous two non-redundant : 691
% 0.14/0.87 % ...aggressively subsumed : 0
% 0.14/0.87 % Contextual simplify-reflections : 13
% 0.14/0.87 % Paramodulations : 793
% 0.14/0.87 % Factorizations : 50
% 0.14/0.87 % NegExts : 0
% 0.14/0.87 % Equation resolutions : 0
% 0.14/0.87 % Disequality decompositions : 0
% 0.14/0.87 % Total rewrite steps : 92
% 0.14/0.87 % ...of those cached : 75
% 0.14/0.87 % Propositional unsat checks : 0
% 0.14/0.87 % Propositional check models : 0
% 0.14/0.87 % Propositional check unsatisfiable : 0
% 0.14/0.87 % Propositional clauses : 0
% 0.14/0.87 % Propositional clauses after purity: 0
% 0.14/0.87 % Propositional unsat core size : 0
% 0.14/0.87 % Propositional preprocessing time : 0.000
% 0.14/0.87 % Propositional encoding time : 0.000
% 0.14/0.87 % Propositional solver time : 0.000
% 0.14/0.87 % Success case prop preproc time : 0.000
% 0.14/0.87 % Success case prop encoding time : 0.000
% 0.14/0.87 % Success case prop solver time : 0.000
% 0.14/0.87 % Current number of processed clauses : 193
% 0.14/0.87 % Positive orientable unit clauses : 18
% 0.14/0.87 % Positive unorientable unit clauses: 0
% 0.14/0.87 % Negative unit clauses : 2
% 0.14/0.87 % Non-unit-clauses : 173
% 0.14/0.87 % Current number of unprocessed clauses: 48
% 0.14/0.87 % ...number of literals in the above : 200
% 0.14/0.87 % Current number of archived formulas : 0
% 0.14/0.87 % Current number of archived clauses : 11
% 0.14/0.87 % Clause-clause subsumption calls (NU) : 13577
% 0.14/0.87 % Rec. Clause-clause subsumption calls : 8295
% 0.14/0.87 % Non-unit clause-clause subsumptions : 448
% 0.14/0.87 % Unit Clause-clause subsumption calls : 527
% 0.14/0.87 % Rewrite failures with RHS unbound : 0
% 0.14/0.87 % BW rewrite match attempts : 45
% 0.14/0.87 % BW rewrite match successes : 1
% 0.14/0.87 % Condensation attempts : 0
% 0.14/0.87 % Condensation successes : 0
% 0.14/0.87 % Termbank termtop insertions : 14352
% 0.14/0.87 % Search garbage collected termcells : 54
% 0.14/0.87
% 0.14/0.87 % -------------------------------------------------
% 0.14/0.87 % User time : 0.025 s
% 0.14/0.87 % System time : 0.006 s
% 0.14/0.87 % Total time : 0.031 s
% 0.14/0.87 % Maximum resident set size: 3648 pages
% 0.14/0.87
% 0.14/0.87 % -------------------------------------------------
% 0.14/0.87 % User time : 0.027 s
% 0.14/0.87 % System time : 0.011 s
% 0.14/0.87 % Total time : 0.038 s
% 0.14/0.87 % Maximum resident set size: 4864 pages
% 0.14/0.87 % E exiting
%------------------------------------------------------------------------------