%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP004-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:23:32 PM UTC 2026
% Result : Unsatisfiable 0.50s 1.61s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP004-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n023.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:17:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.50/1.61 % Version : CSE_E---1.7
% 0.50/1.61 % Problem : theBenchmark.p
% 0.50/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.50/1.61 % SZS output start CNFRefutation
% 0.50/1.61 cnf(associativity1, axiom, (product(X1,X5,X6)|~product(X1,X2,X3)|~product(X2,X4,X5)|~product(X3,X4,X6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', associativity1)).
% 0.50/1.61 cnf(associativity2, axiom, (product(X3,X4,X6)|~product(X1,X2,X3)|~product(X2,X4,X5)|~product(X1,X5,X6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', associativity2)).
% 0.50/1.61 cnf(prove_there_is_a_right_inverse, negated_conjecture, (~product(a,X1,identity)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prove_there_is_a_right_inverse)).
% 0.50/1.61 cnf(left_inverse, axiom, (product(inverse(X1),X1,identity)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', left_inverse)).
% 0.50/1.61 cnf(left_identity, axiom, (product(identity,X1,X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', left_identity)).
% 0.50/1.61 cnf(i_0_5, axiom, (product(X1,X5,X6)|~product(X1,X2,X3)|~product(X2,X4,X5)|~product(X3,X4,X6)), associativity1, ['final']).
% 0.50/1.61 cnf(i_0_6, axiom, (product(X3,X4,X6)|~product(X1,X2,X3)|~product(X2,X4,X5)|~product(X1,X5,X6)), associativity2, ['final']).
% 0.50/1.61 cnf(i_0_7, negated_conjecture, (~product(a,X1,identity)), prove_there_is_a_right_inverse, ['final']).
% 0.50/1.61 cnf(i_0_8, axiom, (product(inverse(X1),X1,identity)), left_inverse, ['final']).
% 0.50/1.61 cnf(i_0_9, axiom, (product(identity,X1,X1)), left_identity, ['final']).
% 0.50/1.68 cnf(i_0_10, plain, (~product(a,identity,inverse(X1))), inference(scs_inference,[],[i_0_7,i_0_9,i_0_8,i_0_5])).
% 0.50/1.68 cnf(i_0_11, plain, (product(inverse(X1),X1,identity)), inference(rename_variables,[],[i_0_8])).
% 0.50/1.68 cnf(i_0_12, plain, (~product(a,X1,identity)), inference(rename_variables,[],[i_0_7])).
% 0.50/1.68 cnf(i_0_13, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X4,X6,X1)|~product(X6,X2,X5)), inference(rename_variables,[],[i_0_5])).
% 0.50/1.68 cnf(i_0_14, plain, (~product(identity,identity,a)), inference(scs_inference,[],[i_0_7,i_0_12,i_0_9,i_0_8,i_0_5,i_0_6])).
% 0.50/1.68 cnf(i_0_15, plain, (product(identity,X1,X1)), inference(rename_variables,[],[i_0_9])).
% 0.50/1.68 cnf(i_0_16, plain, (~product(a,X1,identity)), inference(rename_variables,[],[i_0_7])).
% 0.50/1.68 cnf(i_0_17, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X1,X6,X4)|~product(X6,X5,X2)), inference(rename_variables,[],[i_0_6])).
% 0.50/1.68 cnf(i_0_18, plain, (~product(inverse(identity),inverse(identity),a)), inference(scs_inference,[],[i_0_7,i_0_8,i_0_6])).
% 0.50/1.68 cnf(i_0_19, plain, (product(inverse(X1),X1,identity)), inference(rename_variables,[],[i_0_8])).
% 0.50/1.68 cnf(i_0_20, plain, (~product(a,X1,identity)), inference(rename_variables,[],[i_0_7])).
% 0.50/1.68 cnf(i_0_21, plain, (product(inverse(X1),X1,identity)), inference(rename_variables,[],[i_0_8])).
% 0.50/1.68 cnf(i_0_22, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X1,X6,X4)|~product(X6,X5,X2)), inference(rename_variables,[],[i_0_6])).
% 0.50/1.68 cnf(i_0_23, plain, (~product(a,inverse(X1),inverse(X1))), inference(scs_inference,[],[i_0_7,i_0_20,i_0_8,i_0_21,i_0_6,i_0_5])).
% 0.50/1.68 cnf(i_0_24, plain, (~product(a,X1,identity)), inference(rename_variables,[],[i_0_7])).
% 0.50/1.68 cnf(i_0_25, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X4,X6,X1)|~product(X6,X2,X5)), inference(rename_variables,[],[i_0_5])).
% 0.50/1.68 cnf(i_0_26, plain, (~product(inverse(X1),identity,a)), inference(scs_inference,[],[i_0_7,i_0_9,i_0_8,i_0_6])).
% 0.50/1.68 cnf(i_0_27, plain, (product(inverse(X1),X1,identity)), inference(rename_variables,[],[i_0_8])).
% 0.50/1.68 cnf(i_0_28, plain, (~product(a,X1,identity)), inference(rename_variables,[],[i_0_7])).
% 0.50/1.68 cnf(i_0_29, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X1,X6,X4)|~product(X6,X5,X2)), inference(rename_variables,[],[i_0_6])).
% 0.50/1.68 cnf(i_0_30, plain, (~product(identity,X1,a)|~product(X1,identity,inverse(X2))), inference(scs_inference,[],[i_0_10,i_0_9,i_0_6])).
% 0.50/1.68 cnf(i_0_31, plain, (product(identity,X1,X1)), inference(rename_variables,[],[i_0_9])).
% 0.50/1.68 cnf(i_0_32, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X1,X6,X4)|~product(X6,X5,X2)), inference(rename_variables,[],[i_0_6])).
% 0.50/1.68 cnf(i_0_33, plain, (~product(identity,inverse(a),identity)), inference(scs_inference,[],[i_0_14,i_0_9,i_0_8,i_0_5])).
% 0.50/1.68 cnf(i_0_34, plain, (product(identity,X1,X1)), inference(rename_variables,[],[i_0_9])).
% 0.50/1.68 cnf(i_0_35, plain, (product(inverse(X1),X1,identity)), inference(rename_variables,[],[i_0_8])).
% 0.50/1.68 cnf(i_0_36, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X4,X6,X1)|~product(X6,X2,X5)), inference(rename_variables,[],[i_0_5])).
% 0.50/1.68 cnf(i_0_37, plain, (~product(identity,X1,identity)|~product(X1,identity,a)), inference(scs_inference,[],[i_0_14,i_0_9,i_0_34,i_0_8,i_0_5,i_0_6])).
% 0.50/1.68 cnf(i_0_38, plain, (product(identity,X1,X1)), inference(rename_variables,[],[i_0_9])).
% 0.50/1.68 cnf(i_0_39, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X1,X6,X4)|~product(X6,X5,X2)), inference(rename_variables,[],[i_0_6])).
% 0.50/1.68 cnf(i_0_40, plain, (~product(identity,a,inverse(identity))), inference(scs_inference,[],[i_0_18,i_0_9,i_0_8,i_0_5])).
% 0.50/1.68 cnf(i_0_41, plain, (product(identity,X1,X1)), inference(rename_variables,[],[i_0_9])).
% 0.50/1.68 cnf(i_0_42, plain, (product(inverse(X1),X1,identity)), inference(rename_variables,[],[i_0_8])).
% 0.50/1.68 cnf(i_0_43, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X4,X6,X1)|~product(X6,X2,X5)), inference(rename_variables,[],[i_0_5])).
% 0.50/1.68 cnf(i_0_44, plain, (~product(identity,X1,inverse(identity))|~product(X1,inverse(identity),a)), inference(scs_inference,[],[i_0_18,i_0_9,i_0_41,i_0_8,i_0_5,i_0_6])).
% 0.50/1.68 cnf(i_0_45, plain, (product(identity,X1,X1)), inference(rename_variables,[],[i_0_9])).
% 0.50/1.68 cnf(i_0_46, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X1,X6,X4)|~product(X6,X5,X2)), inference(rename_variables,[],[i_0_6])).
% 0.50/1.68 cnf(i_0_47, plain, (~product(X1,a,identity)), inference(scs_inference,[],[i_0_26,i_0_9,i_0_8,i_0_5])).
% 0.50/1.68 cnf(i_0_48, plain, (product(identity,X1,X1)), inference(rename_variables,[],[i_0_9])).
% 0.50/1.68 cnf(i_0_49, plain, (~product(inverse(X1),identity,a)), inference(rename_variables,[],[i_0_26])).
% 0.50/1.68 cnf(i_0_50, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X4,X6,X1)|~product(X6,X2,X5)), inference(rename_variables,[],[i_0_5])).
% 0.50/1.68 cnf(i_0_51, plain, (~product(identity,X1,inverse(X2))|~product(X1,identity,a)), inference(scs_inference,[],[i_0_26,i_0_49,i_0_9,i_0_48,i_0_8,i_0_5,i_0_6])).
% 0.50/1.68 cnf(i_0_52, plain, (product(identity,X1,X1)), inference(rename_variables,[],[i_0_9])).
% 0.50/1.68 cnf(i_0_53, plain, (~product(X1,X2,X3)|product(X4,X5,X3)|~product(X1,X6,X4)|~product(X6,X5,X2)), inference(rename_variables,[],[i_0_6])).
% 0.50/1.68 cnf(i_0_54,plain, ($false), inference(scs_inference,[],[i_0+47, i_0_8]), ['proof']).
% 0.50/1.68 % SZS output end CNFRefutation
% 0.50/1.68 % Total time : 1.268s
%------------------------------------------------------------------------------