%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 02:15:29 PM UTC 2026
% Result : Unsatisfiable 0.31s 1.04s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 22 ( 9 unt; 6 nHn; 20 RR)
% Number of literals : 41 ( 7 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_2,negated_conjecture,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X1),v_xa(X1),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Relation_Opair__in__Id__conv__iff1_0,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3))
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_Relation_Opair__in__Id__conv__iff1_0) ).
cnf(cls_Relation_OIdI_0,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_Relation_OIdI_0) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X1)),c_Suc(v_xa(X1)),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_1,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_6,negated_conjecture,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X1),v_xa(X1),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_7,plain,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[cls_Relation_Opair__in__Id__conv__iff1_0]) ).
cnf(c_0_8,negated_conjecture,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X1),v_xa(X1),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
c_0_6 ).
cnf(c_0_9,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
cls_Relation_OIdI_0 ).
cnf(c_0_10,negated_conjecture,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X1)),c_Suc(v_xa(X1)),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_3]) ).
cnf(c_0_11,plain,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3))
| X1 = X2 ),
c_0_7 ).
cnf(c_0_12,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X1)),c_Suc(v_xa(X1)),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
c_0_10 ).
cnf(c_0_14,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_xa(c_Relation_OId) = v_x(c_Relation_OId) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
~ v_Q(v_m),
inference(fof_simplification,[status(thm)],[cls_conjecture_1]) ).
cnf(c_0_16,negated_conjecture,
( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_17,negated_conjecture,
( v_m = v_n
| v_xa(c_Relation_OId) = v_x(c_Relation_OId) ),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
~ v_Q(v_m),
c_0_15 ).
cnf(c_0_19,negated_conjecture,
v_m = v_n,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_9])]),c_0_11]) ).
cnf(c_0_20,negated_conjecture,
v_Q(v_n),
cls_conjecture_0 ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n005.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % 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 05:40:03 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.31/1.04 % Version: 3.5.1
% 0.31/1.04 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.31/1.04 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/1.04 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.31/1.04 % Starting new_bool_3 with 300s (1) cores
% 0.31/1.04 % Starting new_bool_1 with 300s (1) cores
% 0.31/1.04 % Starting sh5l with 300s (1) cores
% 0.31/1.04 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2668118 completed with status 0
% 0.31/1.04 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.31/1.04 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.31/1.04 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/1.04 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.31/1.04 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.31/1.04 % No SInE strategy applied
% 0.31/1.04 % Search class: FGHSM-SSLM33-MFFFFFNN
% 0.31/1.04 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.31/1.04 % Starting SubtermCWHack with 136s (1) cores
% 0.31/1.04 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.31/1.04 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S2k with 136s (1) cores
% 0.31/1.04 % Starting new_bool_3 with 136s (1) cores
% 0.31/1.04 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 0.31/1.04 % G-E--_200_B02_F1_AE_CS_SP_PI_S2k with pid 2668125 completed with status 0
% 0.31/1.04 % Result found by G-E--_200_B02_F1_AE_CS_SP_PI_S2k
% 0.31/1.04 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.31/1.04 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/1.04 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.31/1.04 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.31/1.04 % No SInE strategy applied
% 0.31/1.04 % Search class: FGHSM-SSLM33-MFFFFFNN
% 0.31/1.04 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.31/1.04 % Starting SubtermCWHack with 136s (1) cores
% 0.31/1.04 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.31/1.04 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S2k with 136s (1) cores
% 0.31/1.04 % Preprocessing time : 0.017 s
% 0.31/1.04
% 0.31/1.04 % Proof found!
% 0.31/1.04 % SZS status Unsatisfiable
% 0.31/1.04 % SZS output start CNFRefutation
% See solution above
% 0.31/1.04 % Parsed axioms : 1361
% 0.31/1.04 % Removed by relevancy pruning/SinE : 0
% 0.31/1.04 % Initial clauses : 1361
% 0.31/1.04 % Removed in clause preprocessing : 1
% 0.31/1.04 % Initial clauses in saturation : 1360
% 0.31/1.04 % Processed clauses : 2386
% 0.31/1.04 % ...of these trivial : 16
% 0.31/1.04 % ...subsumed : 417
% 0.31/1.04 % ...remaining for further processing : 1953
% 0.31/1.04 % Other redundant clauses eliminated : 4
% 0.31/1.04 % Clauses deleted for lack of memory : 0
% 0.31/1.04 % Backward-subsumed : 14
% 0.31/1.04 % Backward-rewritten : 47
% 0.31/1.04 % Generated clauses : 5684
% 0.31/1.04 % ...of the previous two non-redundant : 4235
% 0.31/1.04 % ...aggressively subsumed : 0
% 0.31/1.04 % Contextual simplify-reflections : 3
% 0.31/1.04 % Paramodulations : 5645
% 0.31/1.04 % Factorizations : 2
% 0.31/1.04 % NegExts : 0
% 0.31/1.04 % Equation resolutions : 37
% 0.31/1.04 % Disequality decompositions : 0
% 0.31/1.04 % Total rewrite steps : 1933
% 0.31/1.04 % ...of those cached : 1520
% 0.31/1.04 % Propositional unsat checks : 0
% 0.31/1.04 % Propositional check models : 0
% 0.31/1.04 % Propositional check unsatisfiable : 0
% 0.31/1.04 % Propositional clauses : 0
% 0.31/1.04 % Propositional clauses after purity: 0
% 0.31/1.04 % Propositional unsat core size : 0
% 0.31/1.04 % Propositional preprocessing time : 0.000
% 0.31/1.04 % Propositional encoding time : 0.000
% 0.31/1.04 % Propositional solver time : 0.000
% 0.31/1.04 % Success case prop preproc time : 0.000
% 0.31/1.04 % Success case prop encoding time : 0.000
% 0.31/1.04 % Success case prop solver time : 0.000
% 0.31/1.04 % Current number of processed clauses : 1892
% 0.31/1.04 % Positive orientable unit clauses : 324
% 0.31/1.04 % Positive unorientable unit clauses: 1
% 0.31/1.04 % Negative unit clauses : 221
% 0.31/1.04 % Non-unit-clauses : 1346
% 0.31/1.04 % Current number of unprocessed clauses: 3157
% 0.31/1.04 % ...number of literals in the above : 5460
% 0.31/1.04 % Current number of archived formulas : 0
% 0.31/1.04 % Current number of archived clauses : 61
% 0.31/1.04 % Clause-clause subsumption calls (NU) : 491754
% 0.31/1.04 % Rec. Clause-clause subsumption calls : 464074
% 0.31/1.04 % Non-unit clause-clause subsumptions : 362
% 0.31/1.04 % Unit Clause-clause subsumption calls : 16125
% 0.31/1.04 % Rewrite failures with RHS unbound : 0
% 0.31/1.04 % BW rewrite match attempts : 502
% 0.31/1.04 % BW rewrite match successes : 48
% 0.31/1.04 % Condensation attempts : 0
% 0.31/1.04 % Condensation successes : 0
% 0.31/1.04 % Termbank termtop insertions : 121581
% 0.31/1.04 % Search garbage collected termcells : 1596
% 0.31/1.04
% 0.31/1.04 % -------------------------------------------------
% 0.31/1.04 % User time : 0.411 s
% 0.31/1.04 % System time : 0.028 s
% 0.31/1.04 % Total time : 0.439 s
% 0.31/1.04 % Maximum resident set size: 5576 pages
% 0.31/1.04
% 0.31/1.04 % -------------------------------------------------
% 0.31/1.04 % User time : 1.551 s
% 0.31/1.04 % System time : 0.071 s
% 0.31/1.04 % Total time : 1.623 s
% 0.31/1.04 % Maximum resident set size: 5376 pages
% 0.31/1.04 % E exiting
%------------------------------------------------------------------------------