%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : COL088-2 : 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 : n017.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 12:10:04 PM UTC 2026
% Result : Unsatisfiable 17.83s 3.39s
% Output : CNFRefutation 17.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 35 ( 14 unt; 0 nHn; 33 RR)
% Number of literals : 75 ( 0 equ; 44 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(reduction_rls_3,axiom,
( ~ member(pair(comb_app(X2,X3),X4),rtrancl(contract))
| ~ member(X3,comb)
| ~ member(pair(X1,X2),contract)
| member(pair(comb_app(X1,X3),X4),rtrancl(contract)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduction_rls_3) ).
cnf(reduction_refl,axiom,
( ~ member(X1,comb)
| member(pair(X1,X1),rtrancl(contract)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduction_refl) ).
cnf(ap_E2,axiom,
( ~ member(comb_app(X1,X2),comb)
| member(X2,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E2) ).
cnf(transD,axiom,
( ~ member(pair(X3,X4),X1)
| ~ member(pair(X2,X3),X1)
| ~ trans(X1)
| member(pair(X2,X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transD) ).
cnf(trans_rtrancl,axiom,
trans(rtrancl(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_rtrancl) ).
cnf(ap_reduce1_2c1,negated_conjecture,
~ member(pair(comb_app(p,r),comb_app(z,r)),rtrancl(contract)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_reduce1_2c1) ).
cnf(ap_reduce1_2h5,hypothesis,
member(pair(comb_app(p,r),comb_app(y,r)),rtrancl(contract)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_reduce1_2h5) ).
cnf(contract_combD2,axiom,
( ~ member(pair(X1,X2),contract)
| member(X2,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contract_combD2) ).
cnf(ap_reduce1_2h4,hypothesis,
member(pair(y,z),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_reduce1_2h4) ).
cnf(comb_intros3,axiom,
( ~ member(X2,comb)
| ~ member(X1,comb)
| member(comb_app(X1,X2),comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros3) ).
cnf(ap_reduce1_2h1,hypothesis,
member(r,comb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_reduce1_2h1) ).
cnf(c_0_11,plain,
( ~ member(pair(comb_app(X2,X3),X4),rtrancl(contract))
| ~ member(X3,comb)
| ~ member(pair(X1,X2),contract)
| member(pair(comb_app(X1,X3),X4),rtrancl(contract)) ),
inference(fof_simplification,[status(thm)],[reduction_rls_3]) ).
cnf(c_0_12,plain,
( ~ member(X1,comb)
| member(pair(X1,X1),rtrancl(contract)) ),
inference(fof_simplification,[status(thm)],[reduction_refl]) ).
cnf(c_0_13,plain,
( ~ member(comb_app(X1,X2),comb)
| member(X2,comb) ),
inference(fof_simplification,[status(thm)],[ap_E2]) ).
cnf(c_0_14,plain,
( ~ member(pair(X3,X4),X1)
| ~ member(pair(X2,X3),X1)
| ~ trans(X1)
| member(pair(X2,X4),X1) ),
inference(fof_simplification,[status(thm)],[transD]) ).
cnf(c_0_15,plain,
( ~ member(pair(comb_app(X2,X3),X4),rtrancl(contract))
| ~ member(X3,comb)
| ~ member(pair(X1,X2),contract)
| member(pair(comb_app(X1,X3),X4),rtrancl(contract)) ),
c_0_11 ).
cnf(c_0_16,plain,
( ~ member(X1,comb)
| member(pair(X1,X1),rtrancl(contract)) ),
c_0_12 ).
cnf(c_0_17,plain,
( ~ member(comb_app(X1,X2),comb)
| member(X2,comb) ),
c_0_13 ).
cnf(c_0_18,plain,
( ~ member(pair(X3,X4),X1)
| ~ member(pair(X2,X3),X1)
| ~ trans(X1)
| member(pair(X2,X4),X1) ),
c_0_14 ).
cnf(c_0_19,plain,
( ~ member(comb_app(X3,X2),comb)
| ~ member(pair(X1,X3),contract)
| member(pair(comb_app(X1,X2),comb_app(X3,X2)),rtrancl(contract)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_20,axiom,
trans(rtrancl(X1)),
trans_rtrancl ).
cnf(c_0_21,negated_conjecture,
~ member(pair(comb_app(p,r),comb_app(z,r)),rtrancl(contract)),
inference(fof_simplification,[status(thm)],[ap_reduce1_2c1]) ).
cnf(c_0_22,plain,
( ~ member(comb_app(X2,X3),comb)
| ~ member(pair(X4,X2),contract)
| ~ member(pair(X1,comb_app(X4,X3)),rtrancl(contract))
| member(pair(X1,comb_app(X2,X3)),rtrancl(contract)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_23,hypothesis,
member(pair(comb_app(p,r),comb_app(y,r)),rtrancl(contract)),
ap_reduce1_2h5 ).
cnf(c_0_24,plain,
( ~ member(pair(X1,X2),contract)
| member(X2,comb) ),
inference(fof_simplification,[status(thm)],[contract_combD2]) ).
cnf(c_0_25,negated_conjecture,
~ member(pair(comb_app(p,r),comb_app(z,r)),rtrancl(contract)),
c_0_21 ).
cnf(c_0_26,hypothesis,
( ~ member(comb_app(X1,r),comb)
| ~ member(pair(y,X1),contract)
| member(pair(comb_app(p,r),comb_app(X1,r)),rtrancl(contract)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,hypothesis,
member(pair(y,z),contract),
ap_reduce1_2h4 ).
cnf(c_0_28,plain,
( ~ member(X2,comb)
| ~ member(X1,comb)
| member(comb_app(X1,X2),comb) ),
inference(fof_simplification,[status(thm)],[comb_intros3]) ).
cnf(c_0_29,plain,
( ~ member(pair(X1,X2),contract)
| member(X2,comb) ),
c_0_24 ).
cnf(c_0_30,negated_conjecture,
~ member(comb_app(z,r),comb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,plain,
( ~ member(X2,comb)
| ~ member(X1,comb)
| member(comb_app(X1,X2),comb) ),
c_0_28 ).
cnf(c_0_32,hypothesis,
member(r,comb),
ap_reduce1_2h1 ).
cnf(c_0_33,hypothesis,
member(z,comb),
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL088-2 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n017.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 14:05:42 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.55 Running first-order theorem proving
% 0.23/0.55 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
% 17.83/3.39 % Version: 3.5.1
% 17.83/3.39 % Preprocessing class: FSLSSMSMSSSNFFN.
% 17.83/3.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.83/3.39 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 17.83/3.39 % Starting new_bool_3 with 300s (1) cores
% 17.83/3.39 % Starting new_bool_1 with 300s (1) cores
% 17.83/3.39 % Starting sh5l with 300s (1) cores
% 17.83/3.39 % sh5l with pid 2511991 completed with status 0
% 17.83/3.39 % Result found by sh5l
% 17.83/3.39 % Preprocessing class: FSLSSMSMSSSNFFN.
% 17.83/3.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.83/3.39 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 17.83/3.39 % Starting new_bool_3 with 300s (1) cores
% 17.83/3.39 % Starting new_bool_1 with 300s (1) cores
% 17.83/3.39 % Starting sh5l with 300s (1) cores
% 17.83/3.39 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 17.83/3.39 % SinE strategy is gf500_gu_R04_F100_L20000
% 17.83/3.39 % Search class: FGUSF-FFMM32-MFFFFFNN
% 17.83/3.39 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 17.83/3.39 % Starting SubtermCWHack with 31s (1) cores
% 17.83/3.39 % SubtermCWHack with pid 2511994 completed with status 0
% 17.83/3.39 % Result found by SubtermCWHack
% 17.83/3.39 % Preprocessing class: FSLSSMSMSSSNFFN.
% 17.83/3.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.83/3.39 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 17.83/3.39 % Starting new_bool_3 with 300s (1) cores
% 17.83/3.39 % Starting new_bool_1 with 300s (1) cores
% 17.83/3.39 % Starting sh5l with 300s (1) cores
% 17.83/3.39 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 17.83/3.39 % SinE strategy is gf500_gu_R04_F100_L20000
% 17.83/3.39 % Search class: FGUSF-FFMM32-MFFFFFNN
% 17.83/3.39 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 17.83/3.39 % Starting SubtermCWHack with 31s (1) cores
% 17.83/3.39 % Preprocessing time : 0.003 s
% 17.83/3.39
% 17.83/3.39 % Proof found!
% 17.83/3.39 % SZS status Unsatisfiable
% 17.83/3.39 % SZS output start CNFRefutation
% See solution above
% 17.83/3.39 % Parsed axioms : 186
% 17.83/3.39 % Removed by relevancy pruning/SinE : 138
% 17.83/3.39 % Initial clauses : 48
% 17.83/3.39 % Removed in clause preprocessing : 1
% 17.83/3.39 % Initial clauses in saturation : 47
% 17.83/3.39 % Processed clauses : 6728
% 17.83/3.39 % ...of these trivial : 0
% 17.83/3.39 % ...subsumed : 3418
% 17.83/3.39 % ...remaining for further processing : 3310
% 17.83/3.39 % Other redundant clauses eliminated : 136
% 17.83/3.39 % Clauses deleted for lack of memory : 0
% 17.83/3.39 % Backward-subsumed : 33
% 17.83/3.39 % Backward-rewritten : 0
% 17.83/3.39 % Generated clauses : 94927
% 17.83/3.39 % ...of the previous two non-redundant : 94421
% 17.83/3.39 % ...aggressively subsumed : 0
% 17.83/3.39 % Contextual simplify-reflections : 227
% 17.83/3.39 % Paramodulations : 94787
% 17.83/3.39 % Factorizations : 0
% 17.83/3.39 % NegExts : 0
% 17.83/3.39 % Equation resolutions : 140
% 17.83/3.39 % Disequality decompositions : 0
% 17.83/3.39 % Total rewrite steps : 1177
% 17.83/3.39 % ...of those cached : 1168
% 17.83/3.39 % Propositional unsat checks : 0
% 17.83/3.39 % Propositional check models : 0
% 17.83/3.39 % Propositional check unsatisfiable : 0
% 17.83/3.39 % Propositional clauses : 0
% 17.83/3.39 % Propositional clauses after purity: 0
% 17.83/3.39 % Propositional unsat core size : 0
% 17.83/3.39 % Propositional preprocessing time : 0.000
% 17.83/3.39 % Propositional encoding time : 0.000
% 17.83/3.39 % Propositional solver time : 0.000
% 17.83/3.39 % Success case prop preproc time : 0.000
% 17.83/3.39 % Success case prop encoding time : 0.000
% 17.83/3.39 % Success case prop solver time : 0.000
% 17.83/3.39 % Current number of processed clauses : 3277
% 17.83/3.39 % Positive orientable unit clauses : 9
% 17.83/3.39 % Positive unorientable unit clauses: 0
% 17.83/3.39 % Negative unit clauses : 47
% 17.83/3.39 % Non-unit-clauses : 3221
% 17.83/3.39 % Current number of unprocessed clauses: 87666
% 17.83/3.39 % ...number of literals in the above : 449813
% 17.83/3.39 % Current number of archived formulas : 0
% 17.83/3.39 % Current number of archived clauses : 33
% 17.83/3.39 % Clause-clause subsumption calls (NU) : 3791464
% 17.83/3.39 % Rec. Clause-clause subsumption calls : 675793
% 17.83/3.39 % Non-unit clause-clause subsumptions : 2961
% 17.83/3.39 % Unit Clause-clause subsumption calls : 3005
% 17.83/3.39 % Rewrite failures with RHS unbound : 0
% 17.83/3.39 % BW rewrite match attempts : 0
% 17.83/3.39 % BW rewrite match successes : 0
% 17.83/3.39 % Condensation attempts : 0
% 17.83/3.39 % Condensation successes : 0
% 17.83/3.39 % Termbank termtop insertions : 1613948
% 17.83/3.39 % Search garbage collected termcells : 684
% 17.83/3.39
% 17.83/3.39 % -------------------------------------------------
% 17.83/3.39 % User time : 2.619 s
% 17.83/3.39 % System time : 0.051 s
% 17.83/3.39 % Total time : 2.670 s
% 17.83/3.39 % Maximum resident set size: 3788 pages
% 17.83/3.39
% 17.83/3.39 % -------------------------------------------------
% 17.83/3.39 % User time : 2.625 s
% 17.83/3.39 % System time : 0.059 s
% 17.83/3.39 % Total time : 2.684 s
% 17.83/3.39 % Maximum resident set size: 4608 pages
% 17.83/3.39 % E exiting
%------------------------------------------------------------------------------