%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP131-2.002 : TPTP v9.2.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.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 04:24:30 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 40 ( 11 unt; 20 nHn; 40 RR)
% Number of literals : 105 ( 0 equ; 49 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(product_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(qg1_1,negated_conjecture,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X2,X1)
| ~ product(X6,X5,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_1) ).
cnf(qg1_2,negated_conjecture,
( equalish(X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X2,X1)
| ~ product(X6,X5,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_2) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_0_9,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1 ).
cnf(c_0_10,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_11,plain,
( product(X1,e_2,e_2)
| product(X1,e_2,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_13,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_14,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,plain,
( product(X1,e_1,e_2)
| product(X1,e_1,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_16,plain,
( equalish(X1,e_2)
| product(e_2,e_2,e_1)
| ~ product(e_2,X1,e_2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_18,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_19,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_20,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_21,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_22,plain,
( equalish(X1,e_2)
| product(e_1,e_2,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_23,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_24,negated_conjecture,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X2,X1)
| ~ product(X6,X5,X4) ),
qg1_1 ).
cnf(c_0_25,plain,
( equalish(X1,e_2)
| product(e_2,e_1,e_1)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( equalish(X1,e_2)
| product(e_1,e_1,e_1)
| ~ product(e_2,e_1,X2)
| ~ product(e_1,X3,X1)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_28,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_18]) ).
cnf(c_0_29,negated_conjecture,
( equalish(X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X2,X1)
| ~ product(X6,X5,X4) ),
qg1_2 ).
cnf(c_0_30,plain,
( equalish(X1,e_2)
| product(e_2,e_2,e_1)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_31,negated_conjecture,
( equalish(X1,e_2)
| product(e_1,e_1,e_1)
| ~ product(e_1,X2,X1)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( equalish(X1,e_2)
| product(e_1,e_2,e_1)
| ~ product(e_2,e_2,X2)
| ~ product(e_1,X1,X3)
| ~ product(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_33,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_18]) ).
cnf(c_0_34,negated_conjecture,
product(e_1,e_1,e_1),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_18]),c_0_26]) ).
cnf(c_0_35,negated_conjecture,
( equalish(X1,e_2)
| product(e_1,e_2,e_1)
| ~ product(e_1,X1,X2)
| ~ product(X2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_37,negated_conjecture,
( equalish(X1,e_1)
| ~ product(e_1,X1,e_1) ),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
product(e_1,e_2,e_1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_34])]),c_0_18]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP131-2.002 : TPTP v9.2.1. Released v1.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n025.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 18:24:43 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------