%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP038-3 : 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 : n013.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 04:23:38 PM UTC 2026
% Result : Unsatisfiable 0.26s 1.61s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 54)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(closure_of_product_and_inverse,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,inverse(X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(a_times_inverse_b_is_c,hypothesis,
product(a,inverse(b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_inverse_b_is_c) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(closure_of_inverse,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
cnf(prove_c_is_in_subgroup,negated_conjecture,
~ subgroup_member(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_is_in_subgroup) ).
cnf(b_is_in_subgroup,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).
cnf(identity_is_in_subgroup,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
cnf(i_0_15,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1,
[final] ).
cnf(i_0_16,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2,
[final] ).
cnf(i_0_17,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2,
[final] ).
cnf(i_0_18,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,inverse(X2),X3) ),
closure_of_product_and_inverse,
[final] ).
cnf(i_0_19,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1,
[final] ).
cnf(i_0_20,axiom,
product(inverse(X1),X1,identity),
left_inverse,
[final] ).
cnf(i_0_21,axiom,
product(X1,inverse(X1),identity),
right_inverse,
[final] ).
cnf(i_0_22,hypothesis,
product(a,inverse(b),c),
a_times_inverse_b_is_c,
[final] ).
cnf(i_0_23,axiom,
product(identity,X1,X1),
left_identity,
[final] ).
cnf(i_0_24,axiom,
product(X1,identity,X1),
right_identity,
[final] ).
cnf(i_0_25,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
closure_of_inverse,
[final] ).
cnf(i_0_26,negated_conjecture,
~ subgroup_member(c),
prove_c_is_in_subgroup,
[final] ).
cnf(i_0_27,hypothesis,
subgroup_member(b),
b_is_in_subgroup,
[final] ).
cnf(i_0_28,hypothesis,
subgroup_member(a),
a_is_in_subgroup,
[final] ).
cnf(i_0_29,axiom,
subgroup_member(identity),
identity_is_in_subgroup,
[final] ).
cnf(i_0_30,axiom,
X1 = X1 ).
cnf(i_0_31,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_32,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_33,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_34,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_35,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| ~ subgroup_member(X1)
| subgroup_member(X2) ) ).
cnf(i_0_30_001,axiom,
X1 = X1 ).
cnf(i_0_31_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_32_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_33_004,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_34_005,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_35_006,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_36_007,axiom,
( X1 != X2
| ~ subgroup_member(X1)
| subgroup_member(X2) ) ).
cnf(i_0_37,plain,
b != c,
inference(scs_inference,[],[i_0_26,i_0_27,i_0_36]) ).
cnf(i_0_38,plain,
~ product(identity,c,b),
inference(scs_inference,[],[i_0_26,i_0_27,i_0_23,i_0_36,i_0_17]) ).
cnf(i_0_39,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_40,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_41,plain,
c != b,
inference(scs_inference,[],[i_0_26,i_0_27,i_0_23,i_0_39,i_0_36,i_0_17,i_0_35]) ).
cnf(i_0_42,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_43,plain,
subgroup_member(inverse(b)),
inference(scs_inference,[],[i_0_26,i_0_27,i_0_29,i_0_23,i_0_39,i_0_42,i_0_36,i_0_17,i_0_35,i_0_18]) ).
cnf(i_0_44,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_45,plain,
( ~ product(X1,inverse(X2),X3)
| subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_46,plain,
~ product(identity,b,c),
inference(scs_inference,[],[i_0_26,i_0_27,i_0_29,i_0_23,i_0_39,i_0_42,i_0_44,i_0_24,i_0_36,i_0_17,i_0_35,i_0_18,i_0_15]) ).
cnf(i_0_47,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_48,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_49,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_50,plain,
~ product(inverse(b),c,identity),
inference(scs_inference,[],[i_0_26,i_0_27,i_0_29,i_0_23,i_0_39,i_0_42,i_0_44,i_0_24,i_0_48,i_0_21,i_0_36,i_0_17,i_0_35,i_0_18,i_0_15,i_0_16]) ).
cnf(i_0_51,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_52,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_21]) ).
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_16]) ).
cnf(i_0_54,plain,
( X1 != identity
| ~ product(X1,c,b) ),
inference(scs_inference,[],[i_0_26,i_0_27,i_0_29,i_0_23,i_0_39,i_0_42,i_0_44,i_0_24,i_0_48,i_0_21,i_0_36,i_0_17,i_0_35,i_0_18,i_0_15,i_0_16,i_0_33]) ).
cnf(i_0_55,plain,
~ product(identity,c,b),
inference(equality_inference,[],[54]) ).
cnf(i_0_56,plain,
multiply(inverse(X1),X1) = identity,
inference(scs_inference,[],[i_0_19,i_0_20,i_0_17]) ).
cnf(i_0_57,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_58,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_59,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_60,plain,
inverse(b) != c,
inference(scs_inference,[],[i_0_26,i_0_43,i_0_19,i_0_20,i_0_17,i_0_36]) ).
cnf(i_0_61,plain,
multiply(identity,b) != c,
inference(scs_inference,[],[i_0_26,i_0_43,i_0_46,i_0_19,i_0_58,i_0_20,i_0_17,i_0_36,i_0_35]) ).
cnf(i_0_62,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_63,plain,
~ product(multiply(inverse(X1),X1),b,c),
inference(scs_inference,[],[i_0_26,i_0_43,i_0_46,i_0_19,i_0_58,i_0_20,i_0_17,i_0_36,i_0_35,i_0_33]) ).
cnf(i_0_64,plain,
$false,
inference(scs_inference,[],[i_0_26,i_0_43,i_0_28,i_0_46,i_0_27,i_0_19,i_0_58,i_0_20,i_0_22,i_0_17,i_0_36,i_0_35,i_0_33,i_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP038-3 : 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
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:18:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.26/1.61 % Version : CSE_E---1.7
% 0.26/1.61 % Problem : theBenchmark.p
% 0.26/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.26/1.61 % SZS output start CNFRefutation
% See solution above
% 0.26/1.69 % Total time : 1.273s
%------------------------------------------------------------------------------