%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:37:34 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.44s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 20 RR)
% Number of literals : 49 ( 48 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 90 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_substitution3,axiom,
ifeq(equalish(X1,X2),true,ifeq(product(X3,X4,X1),true,product(X3,X4,X2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
cnf(left_identity,axiom,
product(identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(total_function2,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,equalish(X4,X3),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
cnf(a_equals_b,hypothesis,
equalish(a,b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
cnf(associativity1,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(product(X6,X4,X1),true,product(X6,X5,X3),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(associativity2,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
cnf(prove_inverse_substitution,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_substitution) ).
cnf(c_0_9,axiom,
ifeq(equalish(X1,X2),true,ifeq(product(X3,X4,X1),true,product(X3,X4,X2),true),true) = true,
product_substitution3 ).
cnf(c_0_10,axiom,
product(identity,X1,X1) = true,
left_identity ).
cnf(c_0_11,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_12,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,equalish(X4,X3),true),true) = true,
total_function2 ).
cnf(c_0_13,plain,
ifeq(equalish(X1,X2),true,product(identity,X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_14,hypothesis,
equalish(a,b) = true,
a_equals_b ).
cnf(c_0_15,plain,
ifeq(product(identity,X1,X2),true,equalish(X2,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_11]) ).
cnf(c_0_16,hypothesis,
product(identity,a,b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).
cnf(c_0_17,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(product(X6,X4,X1),true,product(X6,X5,X3),true),true),true) = true,
associativity1 ).
cnf(c_0_18,axiom,
product(inverse(X1),X1,identity) = true,
left_inverse ).
cnf(c_0_19,hypothesis,
equalish(b,a) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_11]) ).
cnf(c_0_20,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
associativity2 ).
cnf(c_0_21,plain,
ifeq(product(identity,X1,X2),true,ifeq(product(X3,X1,X4),true,product(inverse(X3),X4,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_11]) ).
cnf(c_0_22,hypothesis,
product(identity,b,a) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_19]),c_0_11]) ).
cnf(c_0_23,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(inverse(X3),X1,X4),true,product(X4,X2,identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_11]) ).
cnf(c_0_24,hypothesis,
ifeq(product(X1,b,X2),true,product(inverse(X1),X2,a),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_11]) ).
cnf(c_0_25,plain,
ifeq(product(inverse(X1),identity,X2),true,product(X2,X1,identity),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_10]),c_0_11]) ).
cnf(c_0_26,hypothesis,
product(inverse(inverse(b)),identity,a) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_18]),c_0_11]) ).
cnf(c_0_27,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,inverse(X2),X1),true,product(X4,identity,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_11]) ).
cnf(c_0_28,hypothesis,
product(a,inverse(b),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_11]) ).
cnf(c_0_29,hypothesis,
ifeq(product(identity,b,X1),true,product(a,identity,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_11]) ).
cnf(c_0_30,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X1,identity),true,product(X4,X3,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_10]),c_0_11]) ).
cnf(c_0_31,hypothesis,
product(a,identity,b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_10]),c_0_11]) ).
cnf(c_0_32,hypothesis,
ifeq(product(X1,a,identity),true,product(X1,b,identity),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_11]) ).
cnf(c_0_33,hypothesis,
product(inverse(a),b,identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_18]),c_0_11]) ).
cnf(c_0_34,hypothesis,
ifeq(product(a,X1,X2),true,ifeq(product(identity,X2,X3),true,product(b,X1,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_11]) ).
cnf(c_0_35,hypothesis,
product(inverse(inverse(a)),identity,a) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_33]),c_0_11]) ).
cnf(c_0_36,hypothesis,
ifeq(product(a,X1,X2),true,product(b,X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_10]),c_0_11]) ).
cnf(c_0_37,hypothesis,
product(a,inverse(a),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_35]),c_0_11]) ).
cnf(c_0_38,plain,
ifeq(product(X1,X2,X3),true,product(inverse(X1),X3,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_10]),c_0_11]) ).
cnf(c_0_39,hypothesis,
product(b,inverse(a),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_11]) ).
cnf(c_0_40,hypothesis,
product(inverse(b),identity,inverse(a)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_11]) ).
cnf(c_0_41,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(inverse(X1),X3,X4),true,product(identity,X2,X4),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_11]) ).
cnf(c_0_42,hypothesis,
product(inverse(inverse(b)),inverse(a),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_40]),c_0_11]) ).
cnf(c_0_43,plain,
ifeq(product(inverse(inverse(X1)),identity,X2),true,product(identity,X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_18]),c_0_11]) ).
cnf(c_0_44,hypothesis,
product(inverse(inverse(inverse(b))),identity,inverse(a)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_42]),c_0_11]) ).
cnf(c_0_45,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
inference(fof_simplification,[status(thm)],[prove_inverse_substitution]) ).
cnf(c_0_46,hypothesis,
product(identity,inverse(b),inverse(a)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_11]) ).
cnf(c_0_47,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
c_0_45 ).
cnf(c_0_48,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_46]),c_0_11]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 20 19:55:36 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.07/0.44 % Version: 3.5.1
% 0.07/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.44 % Starting sh5l with 300s (1) cores
% 0.07/0.44 % new_bool_3 with pid 735663 completed with status 0
% 0.07/0.44 % Result found by new_bool_3
% 0.07/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.44 % Search class: FUUPM-FFSF32-MFFFFFNN
% 0.07/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.44 % SubtermCWHack with pid 735668 completed with status 0
% 0.07/0.44 % Result found by SubtermCWHack
% 0.07/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.44 % Search class: FUUPM-FFSF32-MFFFFFNN
% 0.07/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.44 % Preprocessing time : 0.001 s
% 0.07/0.44
% 0.07/0.44 % Proof found!
% 0.07/0.44 % SZS status Unsatisfiable
% 0.07/0.44 % SZS output start CNFRefutation
% See solution above
% 0.07/0.44 % Parsed axioms : 10
% 0.07/0.44 % Removed by relevancy pruning/SinE : 1
% 0.07/0.44 % Initial clauses : 9
% 0.07/0.44 % Removed in clause preprocessing : 0
% 0.07/0.44 % Initial clauses in saturation : 9
% 0.07/0.44 % Processed clauses : 923
% 0.07/0.44 % ...of these trivial : 290
% 0.07/0.44 % ...subsumed : 0
% 0.07/0.44 % ...remaining for further processing : 633
% 0.07/0.44 % Other redundant clauses eliminated : 0
% 0.07/0.44 % Clauses deleted for lack of memory : 0
% 0.07/0.44 % Backward-subsumed : 0
% 0.07/0.44 % Backward-rewritten : 133
% 0.07/0.44 % Generated clauses : 15339
% 0.07/0.44 % ...of the previous two non-redundant : 9091
% 0.07/0.44 % ...aggressively subsumed : 0
% 0.07/0.44 % Contextual simplify-reflections : 0
% 0.07/0.44 % Paramodulations : 15339
% 0.07/0.44 % Factorizations : 0
% 0.07/0.44 % NegExts : 0
% 0.07/0.44 % Equation resolutions : 0
% 0.07/0.44 % Disequality decompositions : 0
% 0.07/0.44 % Total rewrite steps : 17619
% 0.07/0.44 % ...of those cached : 13380
% 0.07/0.44 % Propositional unsat checks : 0
% 0.07/0.44 % Propositional check models : 0
% 0.07/0.44 % Propositional check unsatisfiable : 0
% 0.07/0.44 % Propositional clauses : 0
% 0.07/0.44 % Propositional clauses after purity: 0
% 0.07/0.44 % Propositional unsat core size : 0
% 0.07/0.44 % Propositional preprocessing time : 0.000
% 0.07/0.44 % Propositional encoding time : 0.000
% 0.07/0.44 % Propositional solver time : 0.000
% 0.07/0.44 % Success case prop preproc time : 0.000
% 0.07/0.44 % Success case prop encoding time : 0.000
% 0.07/0.44 % Success case prop solver time : 0.000
% 0.07/0.44 % Current number of processed clauses : 500
% 0.07/0.44 % Positive orientable unit clauses : 499
% 0.07/0.44 % Positive unorientable unit clauses: 0
% 0.07/0.44 % Negative unit clauses : 1
% 0.07/0.44 % Non-unit-clauses : 0
% 0.07/0.44 % Current number of unprocessed clauses: 8072
% 0.07/0.44 % ...number of literals in the above : 8072
% 0.07/0.44 % Current number of archived formulas : 0
% 0.07/0.44 % Current number of archived clauses : 133
% 0.07/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.44 % Non-unit clause-clause subsumptions : 0
% 0.07/0.44 % Unit Clause-clause subsumption calls : 0
% 0.07/0.44 % Rewrite failures with RHS unbound : 0
% 0.07/0.44 % BW rewrite match attempts : 14174
% 0.07/0.44 % BW rewrite match successes : 133
% 0.07/0.44 % Condensation attempts : 0
% 0.07/0.44 % Condensation successes : 0
% 0.07/0.44 % Termbank termtop insertions : 240984
% 0.07/0.44 % Search garbage collected termcells : 5
% 0.07/0.44
% 0.07/0.44 % -------------------------------------------------
% 0.07/0.44 % User time : 0.093 s
% 0.07/0.44 % System time : 0.009 s
% 0.07/0.44 % Total time : 0.102 s
% 0.07/0.44 % Maximum resident set size: 3636 pages
% 0.07/0.44
% 0.07/0.44 % -------------------------------------------------
% 0.07/0.44 % User time : 0.094 s
% 0.07/0.44 % System time : 0.011 s
% 0.07/0.44 % Total time : 0.105 s
% 0.07/0.44 % Maximum resident set size: 4864 pages
% 0.07/0.44 % E exiting
%------------------------------------------------------------------------------