%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYN013-1 : 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 : n008.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 03:31:19 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.51s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 59 ( 15 unt; 37 nHn; 55 RR)
% Number of literals : 167 ( 96 equ; 60 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_16,negated_conjecture,
( ~ element(X1,k)
| X1 = n
| X1 = m
| X1 = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
cnf(c_2,negated_conjecture,
n != k,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_2) ).
cnf(c_15,negated_conjecture,
( X1 != n
| element(X1,k)
| X1 = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_15) ).
cnf(c_10,negated_conjecture,
( g(X1) != X1
| element(X1,n)
| X1 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_10) ).
cnf(c_12,negated_conjecture,
( element(g(X1),X1)
| element(X1,n)
| X1 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_12) ).
cnf(c_8,negated_conjecture,
( ~ element(X2,X1)
| ~ element(X1,X2)
| X2 = X1
| X2 = m
| element(X1,m)
| X1 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_8) ).
cnf(c_3,negated_conjecture,
k != m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_3) ).
cnf(c_1,negated_conjecture,
m != n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_1) ).
cnf(c_9,negated_conjecture,
( g(X1) != n
| element(X1,n)
| X1 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).
cnf(c_11,negated_conjecture,
( element(X1,g(X1))
| element(X1,n)
| X1 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).
cnf(c_7,negated_conjecture,
( ~ element(X1,m)
| element(f(X1),X1)
| X1 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
cnf(c_5,negated_conjecture,
( f(X1) != X1
| ~ element(X1,m)
| X1 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
cnf(c_4,negated_conjecture,
( f(X1) != m
| ~ element(X1,m)
| X1 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_4) ).
cnf(c_6,negated_conjecture,
( ~ element(X1,m)
| element(X1,f(X1))
| X1 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).
cnf(c_13,negated_conjecture,
( ~ element(X2,X1)
| ~ element(X1,X2)
| ~ element(X1,n)
| X2 = X1
| X2 = n
| X1 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_13) ).
cnf(c_14,negated_conjecture,
( X1 != m
| element(X1,k)
| X1 = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_14) ).
cnf(c_0_16,negated_conjecture,
( ~ element(X1,k)
| X1 = n
| X1 = m
| X1 = k ),
inference(fof_simplification,[status(thm)],[c_16]) ).
cnf(c_0_17,negated_conjecture,
n != k,
inference(fof_simplification,[status(thm)],[c_2]) ).
cnf(c_0_18,negated_conjecture,
( X1 != n
| element(X1,k)
| X1 = k ),
inference(fof_simplification,[status(thm)],[c_15]) ).
cnf(c_0_19,negated_conjecture,
( g(X1) != X1
| element(X1,n)
| X1 = n ),
inference(fof_simplification,[status(thm)],[c_10]) ).
cnf(c_0_20,negated_conjecture,
( ~ element(X1,k)
| X1 = n
| X1 = m
| X1 = k ),
c_0_16 ).
cnf(c_0_21,negated_conjecture,
( element(g(X1),X1)
| element(X1,n)
| X1 = n ),
c_12 ).
cnf(c_0_22,negated_conjecture,
n != k,
c_0_17 ).
cnf(c_0_23,negated_conjecture,
( ~ element(X2,X1)
| ~ element(X1,X2)
| X2 = X1
| X2 = m
| element(X1,m)
| X1 = m ),
inference(fof_simplification,[status(thm)],[c_8]) ).
cnf(c_0_24,negated_conjecture,
( X1 != n
| element(X1,k)
| X1 = k ),
c_0_18 ).
cnf(c_0_25,negated_conjecture,
k != m,
inference(fof_simplification,[status(thm)],[c_3]) ).
cnf(c_0_26,negated_conjecture,
m != n,
inference(fof_simplification,[status(thm)],[c_1]) ).
cnf(c_0_27,negated_conjecture,
( g(X1) != X1
| element(X1,n)
| X1 = n ),
c_0_19 ).
cnf(c_0_28,negated_conjecture,
( element(k,n)
| g(k) = k
| g(k) = n
| g(k) = m ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( ~ element(X2,X1)
| ~ element(X1,X2)
| X2 = X1
| X2 = m
| element(X1,m)
| X1 = m ),
c_0_23 ).
cnf(c_0_30,negated_conjecture,
element(n,k),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_22]) ).
cnf(c_0_31,negated_conjecture,
k != m,
c_0_25 ).
cnf(c_0_32,negated_conjecture,
m != n,
c_0_26 ).
cnf(c_0_33,negated_conjecture,
( g(X1) != n
| element(X1,n)
| X1 = n ),
inference(fof_simplification,[status(thm)],[c_9]) ).
cnf(c_0_34,negated_conjecture,
( element(X1,g(X1))
| element(X1,n)
| X1 = n ),
c_11 ).
cnf(c_0_35,negated_conjecture,
( element(k,n)
| g(k) = m
| g(k) = n ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22]) ).
cnf(c_0_36,negated_conjecture,
( ~ element(k,n)
| element(k,m) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]),c_0_22]) ).
cnf(c_0_37,negated_conjecture,
( ~ element(X1,m)
| element(f(X1),X1)
| X1 = m ),
inference(fof_simplification,[status(thm)],[c_7]) ).
cnf(c_0_38,negated_conjecture,
( g(X1) != n
| element(X1,n)
| X1 = n ),
c_0_33 ).
cnf(c_0_39,negated_conjecture,
( element(k,m)
| g(k) = n ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_22]),c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( f(X1) != X1
| ~ element(X1,m)
| X1 = m ),
inference(fof_simplification,[status(thm)],[c_5]) ).
cnf(c_0_41,negated_conjecture,
( ~ element(X1,m)
| element(f(X1),X1)
| X1 = m ),
c_0_37 ).
cnf(c_0_42,negated_conjecture,
element(k,m),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_22]),c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( f(X1) != m
| ~ element(X1,m)
| X1 = m ),
inference(fof_simplification,[status(thm)],[c_4]) ).
cnf(c_0_44,negated_conjecture,
( f(X1) != X1
| ~ element(X1,m)
| X1 = m ),
c_0_40 ).
cnf(c_0_45,negated_conjecture,
( f(k) = k
| f(k) = n
| f(k) = m ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_41]),c_0_31]),c_0_42])]) ).
cnf(c_0_46,negated_conjecture,
( ~ element(X1,m)
| element(X1,f(X1))
| X1 = m ),
inference(fof_simplification,[status(thm)],[c_6]) ).
cnf(c_0_47,negated_conjecture,
( f(X1) != m
| ~ element(X1,m)
| X1 = m ),
c_0_43 ).
cnf(c_0_48,negated_conjecture,
( f(k) = m
| f(k) = n ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_42])]),c_0_31]) ).
cnf(c_0_49,negated_conjecture,
( ~ element(X2,X1)
| ~ element(X1,X2)
| ~ element(X1,n)
| X2 = X1
| X2 = n
| X1 = n ),
inference(fof_simplification,[status(thm)],[c_13]) ).
cnf(c_0_50,negated_conjecture,
( ~ element(X1,m)
| element(X1,f(X1))
| X1 = m ),
c_0_46 ).
cnf(c_0_51,negated_conjecture,
f(k) = n,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42])]),c_0_31]) ).
cnf(c_0_52,negated_conjecture,
( X1 != m
| element(X1,k)
| X1 = k ),
inference(fof_simplification,[status(thm)],[c_14]) ).
cnf(c_0_53,negated_conjecture,
( ~ element(X2,X1)
| ~ element(X1,X2)
| ~ element(X1,n)
| X2 = X1
| X2 = n
| X1 = n ),
c_0_49 ).
cnf(c_0_54,negated_conjecture,
element(k,n),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_42])]),c_0_31]) ).
cnf(c_0_55,negated_conjecture,
( X1 != m
| element(X1,k)
| X1 = k ),
c_0_52 ).
cnf(c_0_56,negated_conjecture,
( ~ element(k,X1)
| ~ element(X1,k)
| X1 = n
| k = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_22]) ).
cnf(c_0_57,negated_conjecture,
element(m,k),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_55]),c_0_31]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_42])]),c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n008.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 10:40:09 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.48 Running first-order theorem proving
% 0.15/0.49 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
% 0.24/0.51 % Version: 3.5.1
% 0.24/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.51 % Starting sh5l with 300s (1) cores
% 0.24/0.51 % sh5l with pid 773343 completed with status 0
% 0.24/0.51 % Result found by sh5l
% 0.24/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.51 % Starting sh5l with 300s (1) cores
% 0.24/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.24/0.51 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.24/0.51 % Search class: FGUSF-FFSF11-SFFFFFNN
% 0.24/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.51 % SubtermCWHack with pid 773345 completed with status 0
% 0.24/0.51 % Result found by SubtermCWHack
% 0.24/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.51 % Starting sh5l with 300s (1) cores
% 0.24/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.24/0.51 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.24/0.51 % Search class: FGUSF-FFSF11-SFFFFFNN
% 0.24/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.51 % Preprocessing time : 0.002 s
% 0.24/0.51
% 0.24/0.51 % Proof found!
% 0.24/0.51 % SZS status Unsatisfiable
% 0.24/0.51 % SZS output start CNFRefutation
% See solution above
% 0.24/0.51 % Parsed axioms : 16
% 0.24/0.51 % Removed by relevancy pruning/SinE : 0
% 0.24/0.51 % Initial clauses : 16
% 0.24/0.51 % Removed in clause preprocessing : 0
% 0.24/0.51 % Initial clauses in saturation : 16
% 0.24/0.51 % Processed clauses : 34
% 0.24/0.51 % ...of these trivial : 0
% 0.24/0.51 % ...subsumed : 5
% 0.24/0.51 % ...remaining for further processing : 29
% 0.24/0.51 % Other redundant clauses eliminated : 2
% 0.24/0.51 % Clauses deleted for lack of memory : 0
% 0.24/0.51 % Backward-subsumed : 3
% 0.24/0.51 % Backward-rewritten : 3
% 0.24/0.51 % Generated clauses : 45
% 0.24/0.51 % ...of the previous two non-redundant : 32
% 0.24/0.51 % ...aggressively subsumed : 0
% 0.24/0.51 % Contextual simplify-reflections : 2
% 0.24/0.51 % Paramodulations : 37
% 0.24/0.51 % Factorizations : 6
% 0.24/0.51 % NegExts : 0
% 0.24/0.51 % Equation resolutions : 2
% 0.24/0.51 % Disequality decompositions : 0
% 0.24/0.51 % Total rewrite steps : 30
% 0.24/0.51 % ...of those cached : 24
% 0.24/0.51 % Propositional unsat checks : 0
% 0.24/0.51 % Propositional check models : 0
% 0.24/0.51 % Propositional check unsatisfiable : 0
% 0.24/0.51 % Propositional clauses : 0
% 0.24/0.51 % Propositional clauses after purity: 0
% 0.24/0.51 % Propositional unsat core size : 0
% 0.24/0.51 % Propositional preprocessing time : 0.000
% 0.24/0.51 % Propositional encoding time : 0.000
% 0.24/0.51 % Propositional solver time : 0.000
% 0.24/0.51 % Success case prop preproc time : 0.000
% 0.24/0.51 % Success case prop encoding time : 0.000
% 0.24/0.51 % Success case prop solver time : 0.000
% 0.24/0.51 % Current number of processed clauses : 21
% 0.24/0.51 % Positive orientable unit clauses : 6
% 0.24/0.51 % Positive unorientable unit clauses: 0
% 0.24/0.51 % Negative unit clauses : 3
% 0.24/0.51 % Non-unit-clauses : 12
% 0.24/0.51 % Current number of unprocessed clauses: 4
% 0.24/0.51 % ...number of literals in the above : 25
% 0.24/0.51 % Current number of archived formulas : 0
% 0.24/0.51 % Current number of archived clauses : 6
% 0.24/0.51 % Clause-clause subsumption calls (NU) : 21
% 0.24/0.51 % Rec. Clause-clause subsumption calls : 14
% 0.24/0.51 % Non-unit clause-clause subsumptions : 4
% 0.24/0.51 % Unit Clause-clause subsumption calls : 2
% 0.24/0.51 % Rewrite failures with RHS unbound : 0
% 0.24/0.51 % BW rewrite match attempts : 3
% 0.24/0.51 % BW rewrite match successes : 3
% 0.24/0.51 % Condensation attempts : 0
% 0.24/0.51 % Condensation successes : 0
% 0.24/0.51 % Termbank termtop insertions : 1110
% 0.24/0.51 % Search garbage collected termcells : 38
% 0.24/0.51
% 0.24/0.51 % -------------------------------------------------
% 0.24/0.51 % User time : 0.006 s
% 0.24/0.51 % System time : 0.002 s
% 0.24/0.51 % Total time : 0.008 s
% 0.24/0.51 % Maximum resident set size: 3584 pages
% 0.24/0.51
% 0.24/0.51 % -------------------------------------------------
% 0.24/0.51 % User time : 0.008 s
% 0.24/0.51 % System time : 0.008 s
% 0.24/0.51 % Total time : 0.016 s
% 0.24/0.51 % Maximum resident set size: 4608 pages
% 0.24/0.51 % E exiting
%------------------------------------------------------------------------------