%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP006-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.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 0.25s 1.62s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of clauses : 37 ( 26 unt; 0 nHn; 20 RR)
% Number of literals : 70 ( 0 equ; 37 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 71 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
cnf(condition,axiom,
( an_element(X3)
| ~ an_element(X1)
| ~ an_element(X2)
| ~ product(X1,inverse(X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(prove_b_inverse_is_in_set,negated_conjecture,
~ an_element(inverse(the_element)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_inverse_is_in_set) ).
cnf(element_of_set,hypothesis,
an_element(the_element),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_of_set) ).
cnf(i_0_9,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1,
[final] ).
cnf(i_0_10,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2,
[final] ).
cnf(i_0_11,axiom,
( an_element(X3)
| ~ an_element(X1)
| ~ an_element(X2)
| ~ product(X1,inverse(X2),X3) ),
condition,
[final] ).
cnf(i_0_12,axiom,
product(inverse(X1),X1,identity),
left_inverse,
[final] ).
cnf(i_0_13,axiom,
product(X1,inverse(X1),identity),
right_inverse,
[final] ).
cnf(i_0_14,axiom,
product(identity,X1,X1),
left_identity,
[final] ).
cnf(i_0_15,axiom,
product(X1,identity,X1),
right_identity,
[final] ).
cnf(i_0_16,negated_conjecture,
~ an_element(inverse(the_element)),
prove_b_inverse_is_in_set,
[final] ).
cnf(i_0_17,hypothesis,
an_element(the_element),
element_of_set,
[final] ).
cnf(i_0_18,plain,
~ an_element(identity),
inference(scs_inference,[],[i_0_16,i_0_17,i_0_14,i_0_11]) ).
cnf(i_0_19,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_20,plain,
( ~ product(X1,inverse(X2),X3)
| an_element(X3)
| ~ an_element(X1)
| ~ an_element(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_21,plain,
product(inverse(inverse(identity)),identity,identity),
inference(scs_inference,[],[i_0_15,i_0_12,i_0_13,i_0_9]) ).
cnf(i_0_22,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_23,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_24,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_13]) ).
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_9]) ).
cnf(i_0_26,plain,
product(inverse(identity),inverse(identity),identity),
inference(scs_inference,[],[i_0_15,i_0_23,i_0_12,i_0_22,i_0_13,i_0_24,i_0_9,i_0_10]) ).
cnf(i_0_27,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_28,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_29,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_30,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_31,plain,
~ an_element(inverse(inverse(the_element))),
inference(scs_inference,[],[i_0_18,i_0_17,i_0_15,i_0_23,i_0_12,i_0_22,i_0_27,i_0_13,i_0_24,i_0_9,i_0_10,i_0_11]) ).
cnf(i_0_32,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_33,plain,
( ~ product(X1,inverse(X2),X3)
| an_element(X3)
| ~ an_element(X1)
| ~ an_element(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_34,plain,
product(inverse(inverse(identity)),X1,X1),
inference(scs_inference,[],[i_0_21,i_0_14,i_0_9]) ).
cnf(i_0_35,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_36,plain,
$false,
inference(scs_inference,[],[i_0_18,i_0_17,i_0_21,i_0_14,i_0_13,i_0_9,i_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP006-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n016.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 18:16:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.25/1.62 % Version : CSE_E---1.7
% 0.25/1.62 % Problem : theBenchmark.p
% 0.25/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.25/1.62 % SZS output start CNFRefutation
% See solution above
% 0.25/1.66 % Total time : 1.273s
%------------------------------------------------------------------------------