%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL093-1 : 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 : n015.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 12:09:35 PM UTC 2026
% Result : Unsatisfiable 0.04s 0.45s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 59 ( 12 unt; 7 nHn; 59 RR)
% Number of literals : 118 ( 28 equ; 55 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 110 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_app,axiom,
combS != comb_app(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_app) ).
cnf(ap_parcontractE11,axiom,
( ~ ap_parcontractE_c3(X1,X2,X3)
| X1 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X1,X2,X3)),ap_parcontractE_sk1q(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE11) ).
cnf(s_parcontractE2,axiom,
( ~ member(pair(combS,X1),parcontract)
| X1 = combS ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_parcontractE2) ).
cnf(ap_parcontractE12,axiom,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X1,ap_parcontractE_sk2q(X1,X2,X3)),parcontract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE12) ).
cnf(ap_parcontractE1,axiom,
( ~ member(pair(comb_app(X1,X2),X3),parcontract)
| ap_parcontractE_c4(X1,X2,X3)
| ap_parcontractE_c3(X1,X2,X3)
| ap_parcontractE_c2(X1,X2,X3)
| ap_parcontractE_c1(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE1) ).
cnf(s1_parcontractD_c1,negated_conjecture,
( ~ member(pair(p,X1),parcontract)
| r != comb_app(combS,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_parcontractD_c1) ).
cnf(ap_parcontractE13,axiom,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X2,ap_parcontractE_sk2s(X1,X2,X3)),parcontract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE13) ).
cnf(ap_parcontractE14,axiom,
( ~ ap_parcontractE_c4(X1,X2,X3)
| X3 = comb_app(ap_parcontractE_sk2q(X1,X2,X3),ap_parcontractE_sk2s(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE14) ).
cnf(ap_parcontractE3,axiom,
( ~ ap_parcontractE_c1(X1,X2,X3)
| X3 = comb_app(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE3) ).
cnf(s1_parcontractD_h1,hypothesis,
member(pair(comb_app(combS,p),r),parcontract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_parcontractD_h1) ).
cnf(parcontract_intros1,axiom,
( ~ member(X1,comb)
| member(pair(X1,X1),parcontract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros1) ).
cnf(ap_parcontractE6,axiom,
( ~ ap_parcontractE_c2(X1,X2,X3)
| X1 = comb_app(combK,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE6) ).
cnf(ap_parcontractE2,axiom,
( ~ ap_parcontractE_c1(X1,X2,X3)
| member(comb_app(X1,X2),comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE2) ).
cnf(ap_E2,axiom,
( ~ member(comb_app(X1,X2),comb)
| member(X2,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E2) ).
cnf(ap_parcontractE4,axiom,
( ~ ap_parcontractE_c2(X1,X2,X3)
| member(X3,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE4) ).
cnf(c_0_15,plain,
combS != comb_app(X1,X2),
inference(fof_simplification,[status(thm)],[s_app]) ).
cnf(c_0_16,plain,
( ~ ap_parcontractE_c3(X1,X2,X3)
| X1 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X1,X2,X3)),ap_parcontractE_sk1q(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE11]) ).
cnf(c_0_17,plain,
( ~ member(pair(combS,X1),parcontract)
| X1 = combS ),
inference(fof_simplification,[status(thm)],[s_parcontractE2]) ).
cnf(c_0_18,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X1,ap_parcontractE_sk2q(X1,X2,X3)),parcontract) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE12]) ).
cnf(c_0_19,plain,
( ~ member(pair(comb_app(X1,X2),X3),parcontract)
| ap_parcontractE_c4(X1,X2,X3)
| ap_parcontractE_c3(X1,X2,X3)
| ap_parcontractE_c2(X1,X2,X3)
| ap_parcontractE_c1(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE1]) ).
cnf(c_0_20,plain,
combS != comb_app(X1,X2),
c_0_15 ).
cnf(c_0_21,plain,
( ~ ap_parcontractE_c3(X1,X2,X3)
| X1 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X1,X2,X3)),ap_parcontractE_sk1q(X1,X2,X3)) ),
c_0_16 ).
cnf(c_0_22,negated_conjecture,
( ~ member(pair(p,X1),parcontract)
| r != comb_app(combS,X1) ),
inference(fof_simplification,[status(thm)],[s1_parcontractD_c1]) ).
cnf(c_0_23,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X2,ap_parcontractE_sk2s(X1,X2,X3)),parcontract) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE13]) ).
cnf(c_0_24,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| X3 = comb_app(ap_parcontractE_sk2q(X1,X2,X3),ap_parcontractE_sk2s(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE14]) ).
cnf(c_0_25,plain,
( ~ member(pair(combS,X1),parcontract)
| X1 = combS ),
c_0_17 ).
cnf(c_0_26,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X1,ap_parcontractE_sk2q(X1,X2,X3)),parcontract) ),
c_0_18 ).
cnf(c_0_27,plain,
( ~ ap_parcontractE_c1(X1,X2,X3)
| X3 = comb_app(X1,X2) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE3]) ).
cnf(c_0_28,plain,
( ~ member(pair(comb_app(X1,X2),X3),parcontract)
| ap_parcontractE_c4(X1,X2,X3)
| ap_parcontractE_c3(X1,X2,X3)
| ap_parcontractE_c2(X1,X2,X3)
| ap_parcontractE_c1(X1,X2,X3) ),
c_0_19 ).
cnf(c_0_29,hypothesis,
member(pair(comb_app(combS,p),r),parcontract),
s1_parcontractD_h1 ).
cnf(c_0_30,plain,
~ ap_parcontractE_c3(combS,X1,X2),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_31,negated_conjecture,
( ~ member(pair(p,X1),parcontract)
| r != comb_app(combS,X1) ),
c_0_22 ).
cnf(c_0_32,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X2,ap_parcontractE_sk2s(X1,X2,X3)),parcontract) ),
c_0_23 ).
cnf(c_0_33,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| X3 = comb_app(ap_parcontractE_sk2q(X1,X2,X3),ap_parcontractE_sk2s(X1,X2,X3)) ),
c_0_24 ).
cnf(c_0_34,plain,
( ~ ap_parcontractE_c4(combS,X1,X2)
| ap_parcontractE_sk2q(combS,X1,X2) = combS ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
( ~ ap_parcontractE_c1(X1,X2,X3)
| X3 = comb_app(X1,X2) ),
c_0_27 ).
cnf(c_0_36,hypothesis,
( ap_parcontractE_c1(combS,p,r)
| ap_parcontractE_c2(combS,p,r)
| ap_parcontractE_c4(combS,p,r) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( ~ ap_parcontractE_c4(X1,p,X2)
| comb_app(combS,ap_parcontractE_sk2s(X1,p,X2)) != r ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
( ~ ap_parcontractE_c4(combS,X1,X2)
| comb_app(combS,ap_parcontractE_sk2s(combS,X1,X2)) = X2 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
( ~ member(X1,comb)
| member(pair(X1,X1),parcontract) ),
inference(fof_simplification,[status(thm)],[parcontract_intros1]) ).
cnf(c_0_40,plain,
( ~ ap_parcontractE_c2(X1,X2,X3)
| X1 = comb_app(combK,X3) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE6]) ).
cnf(c_0_41,hypothesis,
( ap_parcontractE_c2(combS,p,r)
| ap_parcontractE_c4(combS,p,r)
| comb_app(combS,p) = r ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
~ ap_parcontractE_c4(combS,p,r),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_43,plain,
( ~ member(X1,comb)
| member(pair(X1,X1),parcontract) ),
c_0_39 ).
cnf(c_0_44,plain,
( ~ ap_parcontractE_c2(X1,X2,X3)
| X1 = comb_app(combK,X3) ),
c_0_40 ).
cnf(c_0_45,hypothesis,
( ap_parcontractE_c2(combS,p,r)
| comb_app(combS,p) = r ),
inference(sr,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
( ~ ap_parcontractE_c1(X1,X2,X3)
| member(comb_app(X1,X2),comb) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE2]) ).
cnf(c_0_47,plain,
( ~ member(comb_app(X1,X2),comb)
| member(X2,comb) ),
inference(fof_simplification,[status(thm)],[ap_E2]) ).
cnf(c_0_48,negated_conjecture,
( ~ member(p,comb)
| comb_app(combS,p) != r ),
inference(spm,[status(thm)],[c_0_31,c_0_43]) ).
cnf(c_0_49,hypothesis,
comb_app(combS,p) = r,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_20]) ).
cnf(c_0_50,plain,
( ~ ap_parcontractE_c1(X1,X2,X3)
| member(comb_app(X1,X2),comb) ),
c_0_46 ).
cnf(c_0_51,plain,
( ~ member(comb_app(X1,X2),comb)
| member(X2,comb) ),
c_0_47 ).
cnf(c_0_52,negated_conjecture,
~ member(p,comb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
cnf(c_0_53,plain,
( ~ ap_parcontractE_c2(X1,X2,X3)
| member(X3,comb) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE4]) ).
cnf(c_0_54,hypothesis,
( member(comb_app(combS,p),comb)
| ap_parcontractE_c2(combS,p,r)
| ap_parcontractE_c4(combS,p,r) ),
inference(spm,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_55,hypothesis,
~ member(r,comb),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_49]),c_0_52]) ).
cnf(c_0_56,plain,
( ~ ap_parcontractE_c2(X1,X2,X3)
| member(X3,comb) ),
c_0_53 ).
cnf(c_0_57,hypothesis,
ap_parcontractE_c2(combS,p,r),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_54,c_0_42]),c_0_49]),c_0_55]) ).
cnf(c_0_58,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL093-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 14:13:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.42 Running first-order theorem proving
% 0.04/0.42 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
% 0.04/0.45 % Version: 3.5.1
% 0.04/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.04/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.04/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.04/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.04/0.45 % Starting sh5l with 300s (1) cores
% 0.04/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1662075 completed with status 0
% 0.04/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.04/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.04/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.04/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.04/0.45 % No SInE strategy applied
% 0.04/0.45 % Search class: FGHSF-FFMS32-MFFFFFNN
% 0.04/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.04/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.04/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.04/0.45 % Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.04/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.04/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.04/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1662082 completed with status 0
% 0.04/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.04/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.04/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.04/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.04/0.45 % No SInE strategy applied
% 0.04/0.45 % Search class: FGHSF-FFMS32-MFFFFFNN
% 0.04/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.04/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.04/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.04/0.45 % Preprocessing time : 0.001 s
% 0.04/0.45 % Presaturation interreduction done
% 0.04/0.45
% 0.04/0.45 % Proof found!
% 0.04/0.45 % SZS status Unsatisfiable
% 0.04/0.45 % SZS output start CNFRefutation
% See solution above
% 0.04/0.45 % Parsed axioms : 55
% 0.04/0.45 % Removed by relevancy pruning/SinE : 0
% 0.04/0.45 % Initial clauses : 55
% 0.04/0.45 % Removed in clause preprocessing : 1
% 0.04/0.45 % Initial clauses in saturation : 54
% 0.04/0.45 % Processed clauses : 182
% 0.04/0.45 % ...of these trivial : 2
% 0.04/0.45 % ...subsumed : 9
% 0.04/0.45 % ...remaining for further processing : 171
% 0.04/0.45 % Other redundant clauses eliminated : 63
% 0.04/0.45 % Clauses deleted for lack of memory : 0
% 0.04/0.45 % Backward-subsumed : 2
% 0.04/0.45 % Backward-rewritten : 7
% 0.04/0.45 % Generated clauses : 368
% 0.04/0.45 % ...of the previous two non-redundant : 296
% 0.04/0.45 % ...aggressively subsumed : 0
% 0.04/0.45 % Contextual simplify-reflections : 1
% 0.04/0.45 % Paramodulations : 299
% 0.04/0.45 % Factorizations : 0
% 0.04/0.45 % NegExts : 0
% 0.04/0.45 % Equation resolutions : 65
% 0.04/0.45 % Disequality decompositions : 0
% 0.04/0.45 % Total rewrite steps : 31
% 0.04/0.45 % ...of those cached : 26
% 0.04/0.45 % Propositional unsat checks : 0
% 0.04/0.45 % Propositional check models : 0
% 0.04/0.45 % Propositional check unsatisfiable : 0
% 0.04/0.45 % Propositional clauses : 0
% 0.04/0.45 % Propositional clauses after purity: 0
% 0.04/0.45 % Propositional unsat core size : 0
% 0.04/0.45 % Propositional preprocessing time : 0.000
% 0.04/0.45 % Propositional encoding time : 0.000
% 0.04/0.45 % Propositional solver time : 0.000
% 0.04/0.45 % Success case prop preproc time : 0.000
% 0.04/0.45 % Success case prop encoding time : 0.000
% 0.04/0.45 % Success case prop solver time : 0.000
% 0.04/0.45 % Current number of processed clauses : 106
% 0.04/0.45 % Positive orientable unit clauses : 7
% 0.04/0.45 % Positive unorientable unit clauses: 0
% 0.04/0.45 % Negative unit clauses : 28
% 0.04/0.45 % Non-unit-clauses : 71
% 0.04/0.45 % Current number of unprocessed clauses: 214
% 0.04/0.45 % ...number of literals in the above : 817
% 0.04/0.45 % Current number of archived formulas : 0
% 0.04/0.45 % Current number of archived clauses : 65
% 0.04/0.45 % Clause-clause subsumption calls (NU) : 1331
% 0.04/0.45 % Rec. Clause-clause subsumption calls : 1076
% 0.04/0.45 % Non-unit clause-clause subsumptions : 8
% 0.04/0.45 % Unit Clause-clause subsumption calls : 707
% 0.04/0.45 % Rewrite failures with RHS unbound : 0
% 0.04/0.45 % BW rewrite match attempts : 3
% 0.04/0.45 % BW rewrite match successes : 3
% 0.04/0.45 % Condensation attempts : 0
% 0.04/0.45 % Condensation successes : 0
% 0.04/0.45 % Termbank termtop insertions : 6858
% 0.04/0.45 % Search garbage collected termcells : 100
% 0.04/0.45
% 0.04/0.45 % -------------------------------------------------
% 0.04/0.45 % User time : 0.012 s
% 0.04/0.45 % System time : 0.002 s
% 0.04/0.45 % Total time : 0.014 s
% 0.04/0.45 % Maximum resident set size: 3676 pages
% 0.04/0.45
% 0.04/0.45 % -------------------------------------------------
% 0.04/0.45 % User time : 0.039 s
% 0.04/0.45 % System time : 0.020 s
% 0.04/0.45 % Total time : 0.059 s
% 0.04/0.45 % Maximum resident set size: 4864 pages
% 0.04/0.45 % E exiting
%------------------------------------------------------------------------------