%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP128-4.003 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n014.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 04:24:16 PM UTC 2026
% Result : Unsatisfiable 1.30s 1.72s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of clauses : 68 ( 23 unt; 31 nHn; 68 RR)
% Number of literals : 164 ( 0 equ; 60 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 72 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(qg3,negated_conjecture,
( product(X1,X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(qg3_1,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X1,X3,X4)
| ~ product(X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_1) ).
cnf(qg3_2,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,X1,X3)
| ~ product(X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
cnf(row_surjectivity,axiom,
( product(e_1,X1,X2)
| product(e_2,X1,X2)
| product(e_3,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
cnf(product_total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
cnf(product_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(c_0_16,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1 ).
cnf(c_0_17,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_18,plain,
( product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_20,negated_conjecture,
( product(X1,X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X3,X2,X4) ),
qg3 ).
cnf(c_0_21,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_23,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_24,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(X1,e_1,e_1)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_26,plain,
( equalish(X1,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_1,X1,e_1) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_28,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).
cnf(c_0_29,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X1,X3,X4)
| ~ product(X3,X2,X4) ),
qg3_1 ).
cnf(c_0_30,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,X1,X3)
| ~ product(X4,X2,X1) ),
qg3_2 ).
cnf(c_0_32,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(X1,e_2,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_3,e_3,X1)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,axiom,
( product(e_1,X1,X2)
| product(e_2,X1,X2)
| product(e_3,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
row_surjectivity ).
cnf(c_0_36,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_37,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2 ).
cnf(c_0_38,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_39,plain,
( product(e_3,X1,e_3)
| product(e_2,X1,e_3)
| product(e_1,X1,e_3)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_17]) ).
cnf(c_0_40,negated_conjecture,
( product(e_2,e_2,e_2)
| product(X1,e_2,e_2)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_36]) ).
cnf(c_0_41,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_42,negated_conjecture,
( equalish(X1,e_2)
| product(e_3,e_3,e_3)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( product(e_1,e_3,e_3)
| product(e_2,e_3,e_3)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_39,c_0_17]) ).
cnf(c_0_44,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_45,negated_conjecture,
product(e_2,e_2,e_2),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_46,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_47,negated_conjecture,
( equalish(X1,e_1)
| product(e_1,e_3,e_2)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_48,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_49,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_50,negated_conjecture,
( equalish(X1,e_2)
| ~ product(e_2,X1,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(X1,e_3,e_3)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_29,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_53,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_54,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_44,c_0_50]) ).
cnf(c_0_55,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_56,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_51,c_0_46]) ).
cnf(c_0_57,negated_conjecture,
( product(e_2,e_3,e_3)
| product(X1,e_1,e_2)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_20,c_0_52]) ).
cnf(c_0_58,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_55,c_0_50]) ).
cnf(c_0_60,negated_conjecture,
( equalish(X1,e_3)
| product(e_3,e_3,e_2)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
product(e_2,e_3,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_62,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).
cnf(c_0_63,negated_conjecture,
( equalish(X1,e_1)
| product(e_3,e_3,e_3)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_64,negated_conjecture,
product(e_3,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_65,negated_conjecture,
( equalish(X1,e_2)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
product(e_3,e_3,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_49]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_65]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP128-4.003 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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
% 0.14/0.32 % Computer : n014.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:24:51 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.30/1.72 % Version : CSE_E---1.7
% 1.30/1.72 % Problem : theBenchmark.p
% 1.30/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.30/1.72 % SZS output start CNFRefutation
% See solution above
% 1.30/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------