%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET005-1 : 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 : n002.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 02:12:59 PM UTC 2026
% Result : Unsatisfiable 0.36s 0.46s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 62 ( 15 unt; 14 nHn; 49 RR)
% Number of literals : 145 ( 0 equ; 67 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 101 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(a_intersection_bIc,axiom,
intersection(a,bIc,aIbIc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_bIc) ).
cnf(b_intersection_c,axiom,
intersection(b,c,bIc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_intersection_c) ).
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(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(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(a_intersection_b,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_b) ).
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_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(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(prove_aIb_intersection_c_is_aIbIc,negated_conjecture,
~ intersection(aIb,c,aIbIc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aIb_intersection_c_is_aIbIc) ).
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(c_0_13,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_14,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_15,plain,
( ~ member(X4,X3)
| ~ intersection(X1,X2,X3)
| member(X4,X2) ),
c_0_13 ).
cnf(c_0_16,axiom,
intersection(a,bIc,aIbIc),
a_intersection_bIc ).
cnf(c_0_17,plain,
( ~ member(X4,X3)
| ~ intersection(X1,X2,X3)
| member(X4,X1) ),
c_0_14 ).
cnf(c_0_18,axiom,
intersection(b,c,bIc),
b_intersection_c ).
cnf(c_0_19,plain,
( ~ member(X1,aIbIc)
| member(X1,bIc) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
( member(member_of_1_not_of_2(X1,X2),X1)
| subset(X1,X2) ),
subsets_axiom1 ).
cnf(c_0_21,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_22,plain,
( ~ member(member_of_1_not_of_2(X1,X2),X2)
| subset(X1,X2) ),
inference(fof_simplification,[status(thm)],[subsets_axiom2]) ).
cnf(c_0_23,plain,
( ~ member(X1,bIc)
| member(X1,b) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
( member(member_of_1_not_of_2(aIbIc,X1),bIc)
| subset(aIbIc,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( ~ member(X4,X1)
| ~ member(X4,X2)
| ~ intersection(X1,X2,X3)
| member(X4,X3) ),
c_0_21 ).
cnf(c_0_26,axiom,
intersection(a,b,aIb),
a_intersection_b ).
cnf(c_0_27,plain,
( ~ member(X1,aIbIc)
| member(X1,a) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_28,plain,
( ~ subset(X2,X3)
| ~ member(X1,X2)
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[membership_in_subsets]) ).
cnf(c_0_29,plain,
( ~ member(member_of_1_not_of_2(X1,X2),X2)
| subset(X1,X2) ),
c_0_22 ).
cnf(c_0_30,plain,
( member(member_of_1_not_of_2(aIbIc,X1),b)
| subset(aIbIc,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
( ~ member(X1,a)
| ~ member(X1,b)
| member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( member(member_of_1_not_of_2(aIbIc,X1),a)
| subset(aIbIc,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_33,plain,
( ~ subset(X2,X3)
| ~ member(X1,X2)
| member(X1,X3) ),
c_0_28 ).
cnf(c_0_34,plain,
subset(aIbIc,b),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( member(member_of_1_not_of_2(aIbIc,X1),aIb)
| subset(aIbIc,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_30]) ).
cnf(c_0_36,plain,
( ~ member(X1,aIbIc)
| member(X1,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,axiom,
( member(h(X1,X2,X3),X1)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X3) ),
intersection_axiom1 ).
cnf(c_0_38,plain,
subset(aIbIc,aIb),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_39,plain,
( ~ member(X1,b)
| ~ member(X1,c)
| member(X1,bIc) ),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_40,axiom,
( member(h(X1,X2,X3),X2)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X3) ),
intersection_axiom2 ).
cnf(c_0_41,plain,
( ~ member(X1,aIb)
| member(X1,b) ),
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_42,plain,
( member(h(X1,X2,aIbIc),X1)
| member(h(X1,X2,aIbIc),b)
| intersection(X1,X2,aIbIc) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
~ intersection(aIb,c,aIbIc),
inference(fof_simplification,[status(thm)],[prove_aIb_intersection_c_is_aIbIc]) ).
cnf(c_0_44,plain,
( ~ member(X1,aIbIc)
| member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).
cnf(c_0_45,plain,
( ~ member(X1,a)
| ~ member(X1,bIc)
| member(X1,aIbIc) ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_46,plain,
( ~ member(h(X1,c,X2),b)
| member(h(X1,c,X2),X2)
| member(h(X1,c,X2),bIc)
| intersection(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
( member(h(aIb,X1,aIbIc),b)
| intersection(aIb,X1,aIbIc) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
~ intersection(aIb,c,aIbIc),
c_0_43 ).
cnf(c_0_49,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_50,plain,
( ~ member(X1,a)
| ~ member(X1,bIc)
| member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
member(h(aIb,c,aIbIc),bIc),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_19]) ).
cnf(c_0_52,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_49 ).
cnf(c_0_53,plain,
( ~ member(h(aIb,c,aIbIc),a)
| member(h(aIb,c,aIbIc),aIb) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
( member(h(X1,X2,aIbIc),X1)
| member(h(X1,X2,aIbIc),a)
| intersection(X1,X2,aIbIc) ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_55,plain,
( ~ member(h(X1,X2,aIbIc),X1)
| ~ member(h(X1,X2,aIbIc),X2)
| ~ member(h(X1,X2,aIbIc),a)
| ~ member(h(X1,X2,aIbIc),bIc)
| intersection(X1,X2,aIbIc) ),
inference(spm,[status(thm)],[c_0_52,c_0_45]) ).
cnf(c_0_56,plain,
member(h(aIb,c,aIbIc),aIb),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_48]) ).
cnf(c_0_57,plain,
( ~ member(h(aIb,c,aIbIc),c)
| ~ member(h(aIb,c,aIbIc),a) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_51]),c_0_56])]),c_0_48]) ).
cnf(c_0_58,plain,
( ~ member(X1,bIc)
| member(X1,c) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_59,plain,
~ member(h(aIb,c,aIbIc),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_51])]) ).
cnf(c_0_60,plain,
( ~ member(X1,aIb)
| member(X1,a) ),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_61,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 04:44:02 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.36/0.46 % Version: 3.5.1
% 0.36/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.36/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.36/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.36/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.36/0.46 % Starting sh5l with 300s (1) cores
% 0.36/0.46 % sh5l with pid 2449437 completed with status 0
% 0.36/0.46 % Result found by sh5l
% 0.36/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.36/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.36/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.36/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.36/0.46 % Starting sh5l with 300s (1) cores
% 0.36/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.36/0.46 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.36/0.46 % Search class: FGUNF-FFSS32-SFFFFFNN
% 0.36/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.36/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.36/0.46 % SubtermCWHack with pid 2449444 completed with status 0
% 0.36/0.46 % Result found by SubtermCWHack
% 0.36/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.36/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.36/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.36/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.36/0.46 % Starting sh5l with 300s (1) cores
% 0.36/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.36/0.46 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.36/0.46 % Search class: FGUNF-FFSS32-SFFFFFNN
% 0.36/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.36/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.36/0.46 % Preprocessing time : 0.001 s
% 0.36/0.46
% 0.36/0.46 % Proof found!
% 0.36/0.46 % SZS status Unsatisfiable
% 0.36/0.46 % SZS output start CNFRefutation
% See solution above
% 0.36/0.46 % Parsed axioms : 16
% 0.36/0.46 % Removed by relevancy pruning/SinE : 0
% 0.36/0.46 % Initial clauses : 16
% 0.36/0.46 % Removed in clause preprocessing : 0
% 0.36/0.46 % Initial clauses in saturation : 16
% 0.36/0.46 % Processed clauses : 347
% 0.36/0.46 % ...of these trivial : 35
% 0.36/0.46 % ...subsumed : 125
% 0.36/0.46 % ...remaining for further processing : 187
% 0.36/0.46 % Other redundant clauses eliminated : 0
% 0.36/0.46 % Clauses deleted for lack of memory : 0
% 0.36/0.46 % Backward-subsumed : 2
% 0.36/0.46 % Backward-rewritten : 1
% 0.36/0.46 % Generated clauses : 730
% 0.36/0.46 % ...of the previous two non-redundant : 585
% 0.36/0.46 % ...aggressively subsumed : 0
% 0.36/0.46 % Contextual simplify-reflections : 5
% 0.36/0.46 % Paramodulations : 686
% 0.36/0.46 % Factorizations : 44
% 0.36/0.46 % NegExts : 0
% 0.36/0.46 % Equation resolutions : 0
% 0.36/0.46 % Disequality decompositions : 0
% 0.36/0.46 % Total rewrite steps : 92
% 0.36/0.46 % ...of those cached : 59
% 0.36/0.46 % Propositional unsat checks : 0
% 0.36/0.46 % Propositional check models : 0
% 0.36/0.46 % Propositional check unsatisfiable : 0
% 0.36/0.46 % Propositional clauses : 0
% 0.36/0.46 % Propositional clauses after purity: 0
% 0.36/0.46 % Propositional unsat core size : 0
% 0.36/0.46 % Propositional preprocessing time : 0.000
% 0.36/0.46 % Propositional encoding time : 0.000
% 0.36/0.46 % Propositional solver time : 0.000
% 0.36/0.46 % Success case prop preproc time : 0.000
% 0.36/0.46 % Success case prop encoding time : 0.000
% 0.36/0.46 % Success case prop solver time : 0.000
% 0.36/0.46 % Current number of processed clauses : 184
% 0.36/0.46 % Positive orientable unit clauses : 35
% 0.36/0.46 % Positive unorientable unit clauses: 0
% 0.36/0.46 % Negative unit clauses : 2
% 0.36/0.46 % Non-unit-clauses : 147
% 0.36/0.46 % Current number of unprocessed clauses: 254
% 0.36/0.46 % ...number of literals in the above : 839
% 0.36/0.46 % Current number of archived formulas : 0
% 0.36/0.46 % Current number of archived clauses : 3
% 0.36/0.46 % Clause-clause subsumption calls (NU) : 3043
% 0.36/0.46 % Rec. Clause-clause subsumption calls : 2290
% 0.36/0.46 % Non-unit clause-clause subsumptions : 131
% 0.36/0.46 % Unit Clause-clause subsumption calls : 683
% 0.36/0.46 % Rewrite failures with RHS unbound : 0
% 0.36/0.46 % BW rewrite match attempts : 83
% 0.36/0.46 % BW rewrite match successes : 1
% 0.36/0.46 % Condensation attempts : 0
% 0.36/0.46 % Condensation successes : 0
% 0.36/0.46 % Termbank termtop insertions : 11389
% 0.36/0.46 % Search garbage collected termcells : 36
% 0.36/0.46
% 0.36/0.46 % -------------------------------------------------
% 0.36/0.46 % User time : 0.021 s
% 0.36/0.46 % System time : 0.003 s
% 0.36/0.46 % Total time : 0.024 s
% 0.36/0.46 % Maximum resident set size: 3644 pages
% 0.36/0.46
% 0.36/0.46 % -------------------------------------------------
% 0.36/0.46 % User time : 0.022 s
% 0.36/0.46 % System time : 0.008 s
% 0.36/0.46 % Total time : 0.030 s
% 0.36/0.46 % Maximum resident set size: 4864 pages
% 0.36/0.46 % E exiting
%------------------------------------------------------------------------------