%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL090-1 : 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 : n007.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 12:09:34 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 52 ( 21 unt; 8 nHn; 52 RR)
% Number of literals : 95 ( 26 equ; 44 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 108 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(app_app1,axiom,
( comb_app(X1,X2) != comb_app(X3,X4)
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app1) ).
cnf(ap_contractE12,axiom,
( ~ ap_contractE_c3(X1,X2,X3)
| X3 = comb_app(ap_contractE_sk2q(X1,X2,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE12) ).
cnf(k_contractE,axiom,
~ member(pair(combK,X1),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_contractE) ).
cnf(ap_contractE13,axiom,
( ~ ap_contractE_c4(X1,X2,X3)
| member(pair(X2,ap_contractE_sk3q(X1,X2,X3)),contract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE13) ).
cnf(ap_contractE9,axiom,
( ~ ap_contractE_c2(X1,X2,X3)
| X1 = comb_app(comb_app(combS,ap_contractE_sk1p(X1,X2,X3)),ap_contractE_sk1q(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE9) ).
cnf(ap_contractE10,axiom,
( ~ ap_contractE_c3(X1,X2,X3)
| member(pair(X1,ap_contractE_sk2q(X1,X2,X3)),contract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE10) ).
cnf(ap_contractE1,axiom,
( ~ member(pair(comb_app(X1,X2),X3),contract)
| ap_contractE_c4(X1,X2,X3)
| ap_contractE_c3(X1,X2,X3)
| ap_contractE_c2(X1,X2,X3)
| ap_contractE_c1(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE1) ).
cnf(s_app,axiom,
combS != comb_app(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_app) ).
cnf(i_contract_E,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_contract_E) ).
cnf(s_contractE,axiom,
~ member(pair(combS,X1),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_contractE) ).
cnf(ap_contractE4,axiom,
( ~ ap_contractE_c1(X1,X2,X3)
| X1 = comb_app(combK,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE4) ).
cnf(k_s,axiom,
combK != combS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_s) ).
cnf(c_0_12,plain,
( comb_app(X1,X2) != comb_app(X3,X4)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[app_app1]) ).
cnf(c_0_13,plain,
( ~ ap_contractE_c3(X1,X2,X3)
| X3 = comb_app(ap_contractE_sk2q(X1,X2,X3),X2) ),
inference(fof_simplification,[status(thm)],[ap_contractE12]) ).
cnf(c_0_14,plain,
~ member(pair(combK,X1),contract),
inference(fof_simplification,[status(thm)],[k_contractE]) ).
cnf(c_0_15,plain,
( ~ ap_contractE_c4(X1,X2,X3)
| member(pair(X2,ap_contractE_sk3q(X1,X2,X3)),contract) ),
inference(fof_simplification,[status(thm)],[ap_contractE13]) ).
cnf(c_0_16,plain,
( ~ ap_contractE_c2(X1,X2,X3)
| X1 = comb_app(comb_app(combS,ap_contractE_sk1p(X1,X2,X3)),ap_contractE_sk1q(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[ap_contractE9]) ).
cnf(c_0_17,plain,
( ~ ap_contractE_c3(X1,X2,X3)
| member(pair(X1,ap_contractE_sk2q(X1,X2,X3)),contract) ),
inference(fof_simplification,[status(thm)],[ap_contractE10]) ).
cnf(c_0_18,plain,
( comb_app(X1,X2) != comb_app(X3,X4)
| X1 = X3 ),
c_0_12 ).
cnf(c_0_19,plain,
( ~ ap_contractE_c3(X1,X2,X3)
| X3 = comb_app(ap_contractE_sk2q(X1,X2,X3),X2) ),
c_0_13 ).
cnf(c_0_20,plain,
( ~ member(pair(comb_app(X1,X2),X3),contract)
| ap_contractE_c4(X1,X2,X3)
| ap_contractE_c3(X1,X2,X3)
| ap_contractE_c2(X1,X2,X3)
| ap_contractE_c1(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[ap_contractE1]) ).
cnf(c_0_21,plain,
~ member(pair(combK,X1),contract),
c_0_14 ).
cnf(c_0_22,plain,
( ~ ap_contractE_c4(X1,X2,X3)
| member(pair(X2,ap_contractE_sk3q(X1,X2,X3)),contract) ),
c_0_15 ).
cnf(c_0_23,plain,
combS != comb_app(X1,X2),
inference(fof_simplification,[status(thm)],[s_app]) ).
cnf(c_0_24,plain,
( ~ ap_contractE_c2(X1,X2,X3)
| X1 = comb_app(comb_app(combS,ap_contractE_sk1p(X1,X2,X3)),ap_contractE_sk1q(X1,X2,X3)) ),
c_0_16 ).
cnf(c_0_25,plain,
( ~ ap_contractE_c3(X1,X2,X3)
| member(pair(X1,ap_contractE_sk2q(X1,X2,X3)),contract) ),
c_0_17 ).
cnf(c_0_26,plain,
( ~ ap_contractE_c3(X1,X2,comb_app(X3,X4))
| ap_contractE_sk2q(X1,X2,comb_app(X3,X4)) = X3 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_27,plain,
( ~ member(pair(comb_app(X1,X2),X3),contract)
| ap_contractE_c4(X1,X2,X3)
| ap_contractE_c3(X1,X2,X3)
| ap_contractE_c2(X1,X2,X3)
| ap_contractE_c1(X1,X2,X3) ),
c_0_20 ).
cnf(c_0_28,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
i_contract_E ).
cnf(c_0_29,plain,
~ ap_contractE_c4(X1,combK,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
combS != comb_app(X1,X2),
c_0_23 ).
cnf(c_0_31,plain,
( ~ ap_contractE_c2(comb_app(X1,X2),X3,X4)
| comb_app(combS,ap_contractE_sk1p(comb_app(X1,X2),X3,X4)) = X1 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_24])]) ).
cnf(c_0_32,plain,
( ~ ap_contractE_c3(X1,X3,comb_app(X2,X4))
| member(pair(X1,X2),contract) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_34,plain,
~ ap_contractE_c2(comb_app(combS,X1),X2,X3),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_35,plain,
( ~ ap_contractE_c3(X2,X3,X4)
| ~ ap_contractE_c3(X1,X5,X4)
| member(pair(X1,ap_contractE_sk2q(X2,X3,X4)),contract) ),
inference(spm,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_36,negated_conjecture,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r) ),
inference(sr,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
~ member(pair(combS,X1),contract),
inference(fof_simplification,[status(thm)],[s_contractE]) ).
cnf(c_0_38,negated_conjecture,
( ~ ap_contractE_c3(X1,X2,r)
| member(pair(comb_app(combS,combK),ap_contractE_sk2q(X1,X2,r)),contract)
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
~ member(pair(combS,X1),contract),
c_0_37 ).
cnf(c_0_40,plain,
( ~ ap_contractE_c1(X1,X2,X3)
| X1 = comb_app(combK,X3) ),
inference(fof_simplification,[status(thm)],[ap_contractE4]) ).
cnf(c_0_41,negated_conjecture,
( member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract)
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_42,plain,
~ ap_contractE_c3(combS,X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_25]) ).
cnf(c_0_43,plain,
~ ap_contractE_c2(combS,X1,X2),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24])]) ).
cnf(c_0_44,plain,
( ~ ap_contractE_c1(X1,X2,X3)
| X1 = comb_app(combK,X3) ),
c_0_40 ).
cnf(c_0_45,negated_conjecture,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_41]),c_0_29]),c_0_42]),c_0_43]) ).
cnf(c_0_46,negated_conjecture,
ap_contractE_c1(comb_app(combS,combK),combK,r),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_30]) ).
cnf(c_0_47,negated_conjecture,
comb_app(combS,combK) = comb_app(combK,r),
inference(spm,[status(thm)],[c_0_44,c_0_46]) ).
cnf(c_0_48,plain,
combK != combS,
inference(fof_simplification,[status(thm)],[k_s]) ).
cnf(c_0_49,negated_conjecture,
( comb_app(combK,r) != comb_app(X1,X2)
| combS = X1 ),
inference(spm,[status(thm)],[c_0_18,c_0_47]) ).
cnf(c_0_50,plain,
combK != combS,
c_0_48 ).
cnf(c_0_51,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL090-1 : 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 : n007.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 14:08:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1291703 completed with status 0
% 0.10/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.44 % No SInE strategy applied
% 0.10/0.44 % Search class: FGUSF-FFMS32-MFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.10/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1291708 completed with status 0
% 0.10/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.44 % No SInE strategy applied
% 0.10/0.44 % Search class: FGUSF-FFMS32-MFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.44 % Preprocessing time : 0.001 s
% 0.10/0.44 % Presaturation interreduction done
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 32
% 0.10/0.44 % Removed by relevancy pruning/SinE : 0
% 0.10/0.44 % Initial clauses : 32
% 0.10/0.44 % Removed in clause preprocessing : 1
% 0.10/0.44 % Initial clauses in saturation : 31
% 0.10/0.44 % Processed clauses : 205
% 0.10/0.44 % ...of these trivial : 0
% 0.10/0.44 % ...subsumed : 43
% 0.10/0.44 % ...remaining for further processing : 162
% 0.10/0.44 % Other redundant clauses eliminated : 30
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 5
% 0.10/0.44 % Backward-rewritten : 8
% 0.10/0.44 % Generated clauses : 374
% 0.10/0.44 % ...of the previous two non-redundant : 317
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 6
% 0.10/0.44 % Paramodulations : 340
% 0.10/0.44 % Factorizations : 0
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 33
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 42
% 0.10/0.44 % ...of those cached : 37
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 117
% 0.10/0.44 % Positive orientable unit clauses : 8
% 0.10/0.44 % Positive unorientable unit clauses: 0
% 0.10/0.44 % Negative unit clauses : 19
% 0.10/0.44 % Non-unit-clauses : 90
% 0.10/0.44 % Current number of unprocessed clauses: 172
% 0.10/0.44 % ...number of literals in the above : 679
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 45
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 1712
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 1331
% 0.10/0.44 % Non-unit clause-clause subsumptions : 45
% 0.10/0.44 % Unit Clause-clause subsumption calls : 182
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 3
% 0.10/0.44 % BW rewrite match successes : 2
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 6881
% 0.10/0.44 % Search garbage collected termcells : 55
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.010 s
% 0.10/0.44 % System time : 0.004 s
% 0.10/0.44 % Total time : 0.014 s
% 0.10/0.44 % Maximum resident set size: 3656 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.038 s
% 0.10/0.44 % System time : 0.015 s
% 0.10/0.44 % Total time : 0.053 s
% 0.10/0.44 % Maximum resident set size: 4608 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------