%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL006-7 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:09:18 PM UTC 2026
% Result : Unsatisfiable 130.30s 23.27s
% Output : CNFRefutation 130.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 6 RR)
% Number of literals : 49 ( 48 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 104 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
cnf(k_definition,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
cnf(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
cnf(prove_strong_fixed_point,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_0_4,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_5,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_6,plain,
apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
apply(apply(apply(s,apply(s,apply(k,X1))),X2),X3) = apply(X1,apply(X3,apply(X2,X3))),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_8,plain,
apply(apply(apply(s,k),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_9,plain,
apply(apply(apply(s,apply(apply(s,X1),X2)),X3),X4) = apply(apply(apply(X1,X4),apply(X2,X4)),apply(X3,X4)),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_10,plain,
apply(apply(apply(s,apply(s,apply(k,apply(k,X1)))),X2),X3) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_11,axiom,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),
strong_fixed_point ).
cnf(c_0_12,plain,
apply(apply(apply(s,X1),apply(apply(s,k),X2)),X3) = apply(apply(X1,X3),X3),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_13,plain,
apply(apply(apply(s,X1),apply(k,X2)),X3) = apply(apply(X1,X3),X2),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_14,plain,
apply(apply(apply(s,apply(apply(s,s),X1)),X2),apply(s,apply(k,apply(k,X3)))) = X3,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,X1))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_11]),c_0_5]),c_0_6]),c_0_12]) ).
cnf(c_0_16,plain,
apply(apply(apply(s,apply(s,X1)),X2),apply(k,X3)) = apply(apply(X1,apply(X2,apply(k,X3))),X3),
inference(spm,[status(thm)],[c_0_4,c_0_13]) ).
cnf(c_0_17,plain,
apply(strong_fixed_point,apply(k,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
apply(apply(apply(s,apply(s,X1)),apply(apply(s,k),X2)),X3) = apply(apply(X1,X3),apply(X3,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_12]) ).
cnf(c_0_19,plain,
apply(apply(apply(s,apply(s,X1)),strong_fixed_point),apply(k,X2)) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
apply(apply(apply(apply(s,s),X1),X2),X3) = apply(apply(X2,X3),apply(apply(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_21,plain,
apply(apply(apply(s,apply(s,k)),X1),X2) = apply(X1,X2),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_22,plain,
apply(apply(apply(s,strong_fixed_point),X1),apply(k,X2)) = apply(X2,apply(X1,apply(k,X2))),
inference(spm,[status(thm)],[c_0_4,c_0_17]) ).
cnf(c_0_23,plain,
apply(apply(apply(apply(s,X1),X2),X3),apply(X4,apply(X2,X3))) = apply(apply(apply(s,apply(X1,X3)),X4),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_24,plain,
apply(apply(apply(s,apply(s,strong_fixed_point)),apply(apply(s,k),X1)),apply(k,X2)) = apply(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_5]) ).
cnf(c_0_25,plain,
apply(apply(apply(s,X1),apply(apply(s,k),X2)),X3) = apply(apply(apply(s,apply(s,X1)),strong_fixed_point),apply(k,X3)),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_26,plain,
apply(apply(apply(apply(s,s),apply(apply(s,k),X1)),X2),X3) = apply(apply(X2,X3),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_12]) ).
cnf(c_0_27,plain,
apply(apply(apply(apply(s,s),apply(s,apply(s,k))),X1),X2) = apply(apply(X1,X2),apply(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,X1)) = apply(X1,X1),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_29,plain,
apply(apply(apply(apply(s,s),apply(s,k)),X1),X2) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_12,c_0_4]) ).
cnf(c_0_30,plain,
apply(apply(apply(apply(s,X1),apply(apply(s,X2),X3)),X4),apply(X5,apply(apply(X2,X4),apply(X3,X4)))) = apply(apply(apply(s,apply(X1,X4)),X5),apply(apply(X2,X4),apply(X3,X4))),
inference(spm,[status(thm)],[c_0_23,c_0_4]) ).
cnf(c_0_31,plain,
apply(apply(apply(s,apply(s,apply(s,strong_fixed_point))),strong_fixed_point),apply(k,apply(k,X1))) = apply(X1,X1),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
apply(apply(apply(apply(s,s),apply(apply(s,k),X1)),X2),X3) = apply(apply(apply(apply(s,s),apply(s,apply(s,k))),X2),X3),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
apply(apply(apply(apply(s,s),apply(s,apply(s,k))),X1),X2) = apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,apply(X1,X2))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X1))),X2) = apply(X1,apply(X2,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_29]) ).
cnf(c_0_35,plain,
apply(apply(apply(apply(s,s),apply(s,k)),X1),X2) = apply(apply(apply(s,apply(s,X1)),strong_fixed_point),apply(k,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_36,plain,
apply(apply(X1,apply(apply(apply(s,X2),X3),X4)),apply(X5,apply(apply(X2,X4),apply(X3,X4)))) = apply(apply(apply(s,X1),X5),apply(apply(X2,X4),apply(X3,X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_6]),c_0_5]) ).
cnf(c_0_37,plain,
apply(apply(apply(s,apply(s,apply(s,strong_fixed_point))),strong_fixed_point),apply(k,apply(k,X1))) = apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_38,plain,
apply(apply(apply(apply(s,apply(s,s)),strong_fixed_point),apply(k,apply(apply(s,s),apply(s,k)))),apply(s,apply(k,X1))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_39,plain,
apply(apply(apply(apply(s,apply(s,s)),strong_fixed_point),apply(k,X1)),X2) = apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,apply(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_25]),c_0_33]) ).
cnf(c_0_40,plain,
apply(apply(apply(s,apply(s,apply(s,apply(k,X1)))),strong_fixed_point),apply(k,X2)) = apply(X1,apply(X2,X2)),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
apply(apply(X1,apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,X2))),apply(X3,apply(X2,X2))) = apply(apply(apply(s,X1),X3),apply(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_17]),c_0_13]),c_0_13]),c_0_17]),c_0_17]),c_0_13]),c_0_13]),c_0_17]) ).
cnf(c_0_42,plain,
apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X1))))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
apply(apply(apply(s,apply(s,apply(s,apply(k,X1)))),strong_fixed_point),apply(k,X2)) = apply(X1,apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,X2))),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_44,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(fof_simplification,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_0_45,plain,
apply(apply(X1,apply(strong_fixed_point,X2)),apply(X3,apply(X2,apply(strong_fixed_point,X2)))) = apply(apply(apply(s,X1),X3),apply(X2,apply(strong_fixed_point,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_35]),c_0_43]),c_0_42]),c_0_35]),c_0_43]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
c_0_44 ).
cnf(c_0_47,plain,
apply(X1,apply(strong_fixed_point,X1)) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_45]),c_0_8]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL006-7 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n007.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 14:02:20 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 130.30/23.27 % Version: 3.5.1
% 130.30/23.27 % Preprocessing class: FSSSSMSSSSSNFFN.
% 130.30/23.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 130.30/23.27 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 130.30/23.27 % Starting new_bool_3 with 300s (1) cores
% 130.30/23.27 % Starting new_bool_1 with 300s (1) cores
% 130.30/23.27 % Starting sh5l with 300s (1) cores
% 130.30/23.27 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1281103 completed with status 0
% 130.30/23.27 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 130.30/23.27 % Preprocessing class: FSSSSMSSSSSNFFN.
% 130.30/23.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 130.30/23.27 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 130.30/23.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 130.30/23.27 % No SInE strategy applied
% 130.30/23.27 % Search class: FUUPS-FFSF22-DFFFFFNN
% 130.30/23.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 130.30/23.27 % Starting SubtermCWHack with 136s (1) cores
% 130.30/23.27 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 130.30/23.27 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 130.30/23.27 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 130.30/23.27 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 130.30/23.27 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 1281111 completed with status 0
% 130.30/23.27 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 130.30/23.27 % Preprocessing class: FSSSSMSSSSSNFFN.
% 130.30/23.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 130.30/23.27 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 130.30/23.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 130.30/23.27 % No SInE strategy applied
% 130.30/23.27 % Search class: FUUPS-FFSF22-DFFFFFNN
% 130.30/23.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 130.30/23.27 % Starting SubtermCWHack with 136s (1) cores
% 130.30/23.27 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 130.30/23.27 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 130.30/23.27 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 130.30/23.27 % Preprocessing time : 0.001 s
% 130.30/23.27 % Presaturation interreduction done
% 130.30/23.27
% 130.30/23.27 % Proof found!
% 130.30/23.27 % SZS status Unsatisfiable
% 130.30/23.27 % SZS output start CNFRefutation
% See solution above
% 130.30/23.27 % Parsed axioms : 4
% 130.30/23.27 % Removed by relevancy pruning/SinE : 0
% 130.30/23.27 % Initial clauses : 4
% 130.30/23.27 % Removed in clause preprocessing : 0
% 130.30/23.27 % Initial clauses in saturation : 4
% 130.30/23.27 % Processed clauses : 5776
% 130.30/23.27 % ...of these trivial : 1715
% 130.30/23.27 % ...subsumed : 3114
% 130.30/23.27 % ...remaining for further processing : 947
% 130.30/23.27 % Other redundant clauses eliminated : 0
% 130.30/23.27 % Clauses deleted for lack of memory : 0
% 130.30/23.27 % Backward-subsumed : 1
% 130.30/23.27 % Backward-rewritten : 218
% 130.30/23.27 % Generated clauses : 663871
% 130.30/23.27 % ...of the previous two non-redundant : 629318
% 130.30/23.27 % ...aggressively subsumed : 0
% 130.30/23.27 % Contextual simplify-reflections : 0
% 130.30/23.27 % Paramodulations : 663871
% 130.30/23.27 % Factorizations : 0
% 130.30/23.27 % NegExts : 0
% 130.30/23.27 % Equation resolutions : 0
% 130.30/23.27 % Disequality decompositions : 0
% 130.30/23.27 % Total rewrite steps : 454573
% 130.30/23.27 % ...of those cached : 310862
% 130.30/23.27 % Propositional unsat checks : 0
% 130.30/23.27 % Propositional check models : 0
% 130.30/23.27 % Propositional check unsatisfiable : 0
% 130.30/23.27 % Propositional clauses : 0
% 130.30/23.27 % Propositional clauses after purity: 0
% 130.30/23.27 % Propositional unsat core size : 0
% 130.30/23.27 % Propositional preprocessing time : 0.000
% 130.30/23.27 % Propositional encoding time : 0.000
% 130.30/23.27 % Propositional solver time : 0.000
% 130.30/23.27 % Success case prop preproc time : 0.000
% 130.30/23.27 % Success case prop encoding time : 0.000
% 130.30/23.27 % Success case prop solver time : 0.000
% 130.30/23.27 % Current number of processed clauses : 724
% 130.30/23.27 % Positive orientable unit clauses : 566
% 130.30/23.27 % Positive unorientable unit clauses: 158
% 130.30/23.27 % Negative unit clauses : 0
% 130.30/23.27 % Non-unit-clauses : 0
% 130.30/23.27 % Current number of unprocessed clauses: 622608
% 130.30/23.27 % ...number of literals in the above : 622608
% 130.30/23.27 % Current number of archived formulas : 0
% 130.30/23.27 % Current number of archived clauses : 223
% 130.30/23.27 % Clause-clause subsumption calls (NU) : 0
% 130.30/23.27 % Rec. Clause-clause subsumption calls : 0
% 130.30/23.27 % Non-unit clause-clause subsumptions : 0
% 130.30/23.27 % Unit Clause-clause subsumption calls : 17579
% 130.30/23.27 % Rewrite failures with RHS unbound : 3116
% 130.30/23.27 % BW rewrite match attempts : 208821
% 130.30/23.27 % BW rewrite match successes : 1316
% 130.30/23.27 % Condensation attempts : 0
% 130.30/23.27 % Condensation successes : 0
% 130.30/23.27 % Termbank termtop insertions : 30101787
% 130.30/23.27 % Search garbage collected termcells : 2
% 130.30/23.27
% 130.30/23.27 % -------------------------------------------------
% 130.30/23.27 % User time : 19.412 s
% 130.30/23.27 % System time : 0.569 s
% 130.30/23.27 % Total time : 19.982 s
% 130.30/23.27 % Maximum resident set size: 3636 pages
% 130.30/23.27
% 130.30/23.27 % -------------------------------------------------
% 130.30/23.27 % User time : 105.665 s
% 130.30/23.27 % System time : 3.116 s
% 130.30/23.27 % Total time : 108.780 s
% 130.30/23.27 % Maximum resident set size: 4864 pages
% 130.30/23.27 % E exiting
%------------------------------------------------------------------------------