%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP125-1.003 : 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 : n003.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 04:23:58 PM UTC 2026
% Result : Unsatisfiable 0.27s 1.62s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of clauses : 76 ( 47 unt; 8 nHn; 63 RR)
% Number of literals : 142 ( 0 equ; 76 neg)
% Maximal clause size : 5 ( 1 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 : 108 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(qg3,negated_conjecture,
( product(X3,X4,X1)
| ~ product(X1,X2,X3)
| ~ product(X2,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
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(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_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(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
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_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(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_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(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(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(i_0_15,negated_conjecture,
( product(X3,X4,X1)
| ~ product(X1,X2,X3)
| ~ product(X2,X1,X4) ),
qg3,
[final] ).
cnf(i_0_16,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation,
[final] ).
cnf(i_0_17,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation,
[final] ).
cnf(i_0_18,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2,
[final] ).
cnf(i_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,
[final] ).
cnf(i_0_20,axiom,
product(X1,X1,X1),
product_idempotence,
[final] ).
cnf(i_0_21,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2,
[final] ).
cnf(i_0_22,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1,
[final] ).
cnf(i_0_23,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3,
[final] ).
cnf(i_0_24,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1,
[final] ).
cnf(i_0_25,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3,
[final] ).
cnf(i_0_26,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2,
[final] ).
cnf(i_0_27,axiom,
group_element(e_3),
element_3,
[final] ).
cnf(i_0_28,axiom,
group_element(e_2),
element_2,
[final] ).
cnf(i_0_29,axiom,
group_element(e_1),
element_1,
[final] ).
cnf(i_0_30,plain,
~ product(e_3,e_2,e_2),
inference(scs_inference,[],[i_0_20,i_0_21,i_0_16]) ).
cnf(i_0_31,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_32,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_33,plain,
~ product(e_2,e_3,e_2),
inference(scs_inference,[],[i_0_20,i_0_31,i_0_21,i_0_16,i_0_17]) ).
cnf(i_0_34,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_35,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_36,plain,
~ product(e_2,e_2,e_3),
inference(scs_inference,[],[i_0_20,i_0_31,i_0_34,i_0_21,i_0_16,i_0_17,i_0_18]) ).
cnf(i_0_37,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_38,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_39,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(scs_inference,[],[i_0_20,i_0_31,i_0_34,i_0_21,i_0_27,i_0_28,i_0_16,i_0_17,i_0_18,i_0_19]) ).
cnf(i_0_40,plain,
( product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_41,plain,
~ product(e_3,e_1,e_1),
inference(scs_inference,[],[i_0_20,i_0_22,i_0_16]) ).
cnf(i_0_42,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_43,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_44,plain,
~ product(e_1,e_3,e_1),
inference(scs_inference,[],[i_0_20,i_0_42,i_0_22,i_0_16,i_0_17]) ).
cnf(i_0_45,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_46,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_47,plain,
~ product(e_1,e_1,e_3),
inference(scs_inference,[],[i_0_20,i_0_42,i_0_45,i_0_22,i_0_16,i_0_17,i_0_18]) ).
cnf(i_0_48,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_49,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_50,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_1) ),
inference(scs_inference,[],[i_0_20,i_0_42,i_0_45,i_0_33,i_0_22,i_0_27,i_0_28,i_0_16,i_0_17,i_0_18,i_0_19]) ).
cnf(i_0_51,plain,
( product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_52,plain,
( product(X1,e_3,e_3)
| ~ product(e_3,e_2,X1)
| product(e_2,e_3,e_1) ),
inference(scs_inference,[],[i_0_20,i_0_42,i_0_45,i_0_33,i_0_22,i_0_27,i_0_28,i_0_16,i_0_17,i_0_18,i_0_19,i_0_15]) ).
cnf(i_0_53,plain,
~ product(e_2,e_3,e_3),
inference(scs_inference,[],[i_0_20,i_0_23,i_0_16]) ).
cnf(i_0_54,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_55,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_56,plain,
~ product(e_3,e_2,e_3),
inference(scs_inference,[],[i_0_20,i_0_54,i_0_23,i_0_16,i_0_17]) ).
cnf(i_0_57,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_58,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_59,plain,
~ product(e_3,e_3,e_2),
inference(scs_inference,[],[i_0_20,i_0_54,i_0_57,i_0_23,i_0_16,i_0_17,i_0_18]) ).
cnf(i_0_60,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_61,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_62,plain,
product(e_3,e_2,e_1),
inference(scs_inference,[],[i_0_20,i_0_54,i_0_57,i_0_30,i_0_23,i_0_27,i_0_28,i_0_16,i_0_17,i_0_18,i_0_19]) ).
cnf(i_0_63,plain,
( product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_64,plain,
product(e_2,e_3,e_1),
inference(scs_inference,[],[i_0_20,i_0_54,i_0_57,i_0_30,i_0_23,i_0_27,i_0_28,i_0_16,i_0_17,i_0_18,i_0_19,i_0_50]) ).
cnf(i_0_65,plain,
product(e_1,e_1,e_2),
inference(scs_inference,[],[i_0_20,i_0_54,i_0_57,i_0_30,i_0_23,i_0_27,i_0_28,i_0_16,i_0_17,i_0_18,i_0_19,i_0_50,i_0_15]) ).
cnf(i_0_66,plain,
( ~ product(X1,X2,X3)
| product(X4,X3,X2)
| ~ product(X2,X1,X4) ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_67,plain,
product(e_2,e_2,e_1),
inference(scs_inference,[],[i_0_65,i_0_15]) ).
cnf(i_0_68,plain,
( ~ product(X1,X2,X3)
| product(X4,X3,X2)
| ~ product(X2,X1,X4) ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_69,plain,
~ product(e_2,e_1,e_1),
inference(scs_inference,[],[i_0_20,i_0_65,i_0_24,i_0_15,i_0_16]) ).
cnf(i_0_70,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_71,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_72,plain,
~ product(e_1,e_2,e_1),
inference(scs_inference,[],[i_0_20,i_0_70,i_0_65,i_0_24,i_0_15,i_0_16,i_0_17]) ).
cnf(i_0_73,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_74,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_75,plain,
$false,
inference(scs_inference,[],[i_0_20,i_0_70,i_0_73,i_0_65,i_0_24,i_0_15,i_0_16,i_0_17,i_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP125-1.003 : 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 : n003.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 18:21:41 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.27/1.62 % Version : CSE_E---1.7
% 0.27/1.62 % Problem : theBenchmark.p
% 0.27/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.27/1.62 % SZS output start CNFRefutation
% See solution above
% 0.36/1.72 % Total time : 1.271s
%------------------------------------------------------------------------------