%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP130-3.003 : 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 : n026.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 04:24:28 PM UTC 2026
% Result : Unsatisfiable 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of clauses : 90 ( 27 unt; 32 nHn; 90 RR)
% Number of literals : 212 ( 0 equ; 93 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 79 ( 2 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_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_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(cycle7,axiom,
( equalish(X3,X4)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,X3)
| ~ greater(X2,e_0)
| ~ next(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle7) ).
cnf(cycle2,axiom,
( cycle(X1,e_0)
| cycle(X1,e_1)
| cycle(X1,e_2)
| ~ group_element(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle2) ).
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_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(e_1_greater_e_0,axiom,
greater(e_1,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_greater_e_0) ).
cnf(e_1_then_e_2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
cnf(qg3,negated_conjecture,
( product(X4,X2,X1)
| ~ product(X1,X2,X3)
| ~ product(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
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(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(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_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(cycle6,axiom,
( ~ cycle(X1,e_0)
| ~ product(X1,e_1,X2)
| ~ greater(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle6) ).
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(e_3_greater_e_1,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).
cnf(e_2_greater_e_0,axiom,
greater(e_2,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_0) ).
cnf(c_0_19,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_20,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_21,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_22,axiom,
( equalish(X3,X4)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,X3)
| ~ greater(X2,e_0)
| ~ next(X1,X4) ),
cycle7 ).
cnf(c_0_23,axiom,
( cycle(X1,e_0)
| cycle(X1,e_1)
| cycle(X1,e_2)
| ~ group_element(X1) ),
cycle2 ).
cnf(c_0_24,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_25,plain,
( product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_27,plain,
( ~ product(X1,e_1,e_1)
| ~ cycle(X1,X2)
| ~ greater(X2,e_0)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( cycle(e_1,e_2)
| cycle(e_1,e_1)
| cycle(e_1,e_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_29,axiom,
greater(e_1,e_0),
e_1_greater_e_0 ).
cnf(c_0_30,axiom,
next(e_1,e_2),
e_1_then_e_2 ).
cnf(c_0_31,plain,
( ~ product(X1,e_1,e_3)
| ~ cycle(X1,X2)
| ~ greater(X2,e_0)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_32,negated_conjecture,
( product(X4,X2,X1)
| ~ product(X1,X2,X3)
| ~ product(X1,X3,X4) ),
qg3 ).
cnf(c_0_33,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
( cycle(e_1,e_0)
| cycle(e_1,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_35,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_36,plain,
( cycle(e_1,e_0)
| cycle(e_1,e_2)
| ~ product(e_1,e_1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_29]),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_1,e_3)
| product(e_3,e_1,e_2)
| product(e_1,X1,e_3)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_40,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_41,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_42,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_19,c_0_26]) ).
cnf(c_0_43,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_44,axiom,
( ~ cycle(X1,e_0)
| ~ product(X1,e_1,X2)
| ~ greater(X2,X1) ),
cycle6 ).
cnf(c_0_45,plain,
( product(e_1,e_1,e_2)
| cycle(e_1,e_2)
| cycle(e_1,e_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_46,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_47,negated_conjecture,
( product(e_1,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_38,c_0_33]) ).
cnf(c_0_48,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_50,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_41]) ).
cnf(c_0_51,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_42,c_0_26]) ).
cnf(c_0_52,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_19,c_0_43]) ).
cnf(c_0_53,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_43]) ).
cnf(c_0_54,plain,
( product(e_1,e_1,e_2)
| cycle(e_1,e_2)
| ~ product(e_1,e_1,X1)
| ~ greater(X1,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,axiom,
greater(e_3,e_1),
e_3_greater_e_1 ).
cnf(c_0_56,negated_conjecture,
( product(e_3,e_1,e_3)
| ~ product(e_1,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_57,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_40]) ).
cnf(c_0_58,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_40]) ).
cnf(c_0_59,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_52,c_0_26]) ).
cnf(c_0_61,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| ~ product(e_3,X1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_51]),c_0_48]) ).
cnf(c_0_62,negated_conjecture,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_1,X1,e_2)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_32,c_0_53]) ).
cnf(c_0_63,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| cycle(e_1,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_47]),c_0_55])]),c_0_56]) ).
cnf(c_0_64,axiom,
greater(e_2,e_0),
e_2_greater_e_0 ).
cnf(c_0_65,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_66,negated_conjecture,
( product(e_3,e_1,e_2)
| ~ product(e_2,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_47]),c_0_58]) ).
cnf(c_0_67,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_62,c_0_53]) ).
cnf(c_0_69,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_41]) ).
cnf(c_0_70,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_63]),c_0_64]),c_0_30])]),c_0_47]) ).
cnf(c_0_71,negated_conjecture,
( ~ product(e_3,e_3,e_2)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
( product(e_3,e_3,e_2)
| ~ product(e_3,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_67]),c_0_46]) ).
cnf(c_0_73,negated_conjecture,
( product(e_2,e_1,e_3)
| ~ product(e_3,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_68]),c_0_58]) ).
cnf(c_0_74,negated_conjecture,
( product(e_3,e_1,e_2)
| ~ product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
( ~ product(e_2,e_1,e_3)
| ~ product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_77,negated_conjecture,
~ product(e_3,e_2,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_78,negated_conjecture,
( product(e_3,e_1,e_2)
| ~ product(e_3,X1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_70]),c_0_76]) ).
cnf(c_0_79,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_60,c_0_77]) ).
cnf(c_0_80,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_81,negated_conjecture,
~ product(e_3,e_3,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_80]),c_0_50]) ).
cnf(c_0_82,negated_conjecture,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_1,X1,e_3)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_32,c_0_60]) ).
cnf(c_0_83,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_51,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( product(e_3,e_1,e_2)
| ~ product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_70]) ).
cnf(c_0_85,negated_conjecture,
( product(e_1,e_1,e_3)
| product(e_3,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_80]),c_0_77]) ).
cnf(c_0_86,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_73,c_0_80]) ).
cnf(c_0_87,negated_conjecture,
product(e_3,e_1,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_83]),c_0_84]) ).
cnf(c_0_88,negated_conjecture,
product(e_3,e_2,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_85]),c_0_86]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_87]),c_0_88])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP130-3.003 : 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 : n026.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 18:24:08 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
% 1.29/1.74 % Total time : 1.374s
%------------------------------------------------------------------------------