%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP001-5 : 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 : n031.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 04:23:30 PM UTC 2026
% Result : Unsatisfiable 0.77s 1.62s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 63 ( 33 unt; 0 nHn; 39 RR)
% Number of literals : 131 ( 0 equ; 82 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 148 ( 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/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity2) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(square_element,hypothesis,
product(X1,X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_element) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(i_0_7,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1,
[final] ).
cnf(i_0_8,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2,
[final] ).
cnf(i_0_9,negated_conjecture,
~ product(b,a,c),
prove_b_times_a_is_c,
[final] ).
cnf(i_0_10,axiom,
product(identity,X1,X1),
left_identity,
[final] ).
cnf(i_0_11,axiom,
product(X1,identity,X1),
right_identity,
[final] ).
cnf(i_0_12,hypothesis,
product(X1,X1,identity),
square_element,
[final] ).
cnf(i_0_13,hypothesis,
product(a,b,c),
a_times_b_is_c,
[final] ).
cnf(i_0_14,plain,
~ product(b,c,a),
inference(scs_inference,[],[i_0_9,i_0_10,i_0_12,i_0_7]) ).
cnf(i_0_15,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_16,plain,
product(X1,X1,identity),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_17,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_18,plain,
~ product(c,a,b),
inference(scs_inference,[],[i_0_9,i_0_10,i_0_11,i_0_12,i_0_16,i_0_7,i_0_8]) ).
cnf(i_0_19,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_20,plain,
product(X1,X1,identity),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_21,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_22,plain,
( ~ product(b,X1,a)
| ~ product(X1,b,a) ),
inference(scs_inference,[],[i_0_9,i_0_13,i_0_7]) ).
cnf(i_0_23,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_24,plain,
( ~ product(a,X1,b)
| ~ product(X1,a,b) ),
inference(scs_inference,[],[i_0_9,i_0_13,i_0_7,i_0_8]) ).
cnf(i_0_25,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_26,plain,
( ~ product(b,X1,c)
| ~ product(X1,identity,a) ),
inference(scs_inference,[],[i_0_9,i_0_11,i_0_7]) ).
cnf(i_0_27,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_28,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_29,plain,
( ~ product(identity,X1,b)
| ~ product(X1,a,c) ),
inference(scs_inference,[],[i_0_9,i_0_11,i_0_10,i_0_7,i_0_8]) ).
cnf(i_0_30,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_31,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_32,plain,
( product(a,X1,identity)
| ~ product(b,c,X1) ),
inference(scs_inference,[],[i_0_13,i_0_12,i_0_7]) ).
cnf(i_0_33,plain,
product(X1,X1,identity),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_34,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_35,plain,
( product(a,identity,identity)
| ~ product(identity,c,b) ),
inference(scs_inference,[],[i_0_13,i_0_11,i_0_12,i_0_33,i_0_7,i_0_8]) ).
cnf(i_0_36,plain,
product(X1,X1,identity),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_37,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_38,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_39,plain,
( product(c,X1,identity)
| ~ product(b,X1,a) ),
inference(scs_inference,[],[i_0_13,i_0_12,i_0_8]) ).
cnf(i_0_40,plain,
product(X1,X1,identity),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_41,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_42,plain,
~ product(a,c,b),
inference(scs_inference,[],[i_0_14,i_0_12,i_0_11,i_0_8]) ).
cnf(i_0_43,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_44,plain,
product(X1,X1,identity),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_45,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_46,plain,
( ~ product(b,X1,a)
| ~ product(X1,identity,c) ),
inference(scs_inference,[],[i_0_14,i_0_12,i_0_11,i_0_43,i_0_8,i_0_7]) ).
cnf(i_0_47,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_48,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_49,plain,
( ~ product(identity,X1,b)
| ~ product(X1,c,a) ),
inference(scs_inference,[],[i_0_14,i_0_10,i_0_8]) ).
cnf(i_0_50,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_51,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_52,plain,
~ product(c,b,a),
inference(scs_inference,[],[i_0_18,i_0_10,i_0_12,i_0_7]) ).
cnf(i_0_53,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_54,plain,
product(X1,X1,identity),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_55,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_56,plain,
( ~ product(identity,X1,c)
| ~ product(X1,a,b) ),
inference(scs_inference,[],[i_0_18,i_0_10,i_0_53,i_0_12,i_0_7,i_0_8]) ).
cnf(i_0_57,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_58,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_59,plain,
( ~ product(c,X1,b)
| ~ product(X1,identity,a) ),
inference(scs_inference,[],[i_0_18,i_0_11,i_0_7]) ).
cnf(i_0_60,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_61,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_62,plain,
$false,
inference(scs_inference,[],[i_0_42,i_0_12,i_0_13,i_0_10,i_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP001-5 : 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 : n031.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 18:17:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.77/1.62 % Version : CSE_E---1.7
% 0.77/1.62 % Problem : theBenchmark.p
% 0.77/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.77/1.62 % SZS output start CNFRefutation
% See solution above
% 0.77/1.69 % Total time : 1.268s
%------------------------------------------------------------------------------