%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP124-2.004 : TPTP v9.2.1. Released v1.2.0.
% 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 : n001.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 04:23:57 PM UTC 2026
% Result : Unsatisfiable 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of clauses : 86 ( 30 unt; 32 nHn; 84 RR)
% Number of literals : 203 ( 0 equ; 86 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 70 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
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(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(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(qg2_1,negated_conjecture,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X1,X2)
| ~ product(X6,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_1) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
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(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_0_15,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1 ).
cnf(c_0_16,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_17,axiom,
~ equalish(e_4,e_3),
e_4_is_not_e_3 ).
cnf(c_0_18,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_19,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_20,plain,
( product(X1,e_4,e_4)
| product(X1,e_4,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_22,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_24,axiom,
~ equalish(e_4,e_2),
e_4_is_not_e_2 ).
cnf(c_0_25,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_26,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_27,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
~ product(e_3,e_4,e_4),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_30,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_31,plain,
( product(X1,e_3,e_4)
| 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_15,c_0_21]) ).
cnf(c_0_32,plain,
~ product(e_4,e_3,e_4),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_33,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_34,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_36,plain,
~ product(e_2,e_4,e_4),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_37,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_16]),c_0_32]) ).
cnf(c_0_38,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_39,plain,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_40,negated_conjecture,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X1,X2)
| ~ product(X6,X4,X5) ),
qg2_1 ).
cnf(c_0_41,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_44,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X3)
| ~ product(e_2,X2,X4)
| ~ product(e_3,X3,X4) ),
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_46,plain,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,axiom,
~ equalish(e_4,e_1),
e_4_is_not_e_1 ).
cnf(c_0_48,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_49,negated_conjecture,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_4,X3)
| ~ product(e_2,X2,X4)
| ~ product(e_4,X3,X4) ),
inference(spm,[status(thm)],[c_0_24,c_0_40]) ).
cnf(c_0_50,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( ~ product(e_2,e_3,X1)
| ~ product(e_2,e_2,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_23]) ).
cnf(c_0_52,plain,
( product(e_3,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_46]),c_0_23])]) ).
cnf(c_0_53,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_54,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_19]) ).
cnf(c_0_55,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_19]) ).
cnf(c_0_56,negated_conjecture,
( ~ product(e_2,e_4,X1)
| ~ product(e_2,e_2,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_23]) ).
cnf(c_0_57,plain,
( product(e_4,e_3,e_2)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_50]),c_0_23])]) ).
cnf(c_0_58,plain,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_25,c_0_42]) ).
cnf(c_0_59,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| ~ product(e_2,e_3,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_23])]) ).
cnf(c_0_60,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_20,c_0_53]) ).
cnf(c_0_61,plain,
~ product(e_1,e_4,e_1),
inference(spm,[status(thm)],[c_0_54,c_0_23]) ).
cnf(c_0_62,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_63,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_31,c_0_53]) ).
cnf(c_0_64,plain,
~ product(e_1,e_3,e_1),
inference(spm,[status(thm)],[c_0_55,c_0_23]) ).
cnf(c_0_65,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_4)
| ~ product(e_2,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_23])]) ).
cnf(c_0_66,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_44]),c_0_59]) ).
cnf(c_0_67,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_18]) ).
cnf(c_0_68,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_18]) ).
cnf(c_0_70,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_72,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_23])]) ).
cnf(c_0_74,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_23])]) ).
cnf(c_0_76,plain,
( product(e_1,e_4,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_69,c_0_73]) ).
cnf(c_0_77,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_18]) ).
cnf(c_0_78,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_23])]) ).
cnf(c_0_81,negated_conjecture,
( product(e_2,e_3,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_82,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_81,c_0_66]) ).
cnf(c_0_83,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_84,negated_conjecture,
product(e_2,e_3,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_82]),c_0_23])]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP124-2.004 : TPTP v9.2.1. Released v1.2.0.
% 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 : n001.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 18:23:03 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------