%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP037-3 : TPTP v9.2.1. Released v1.0.0.
% 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 : n028.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 04:23:38 PM UTC 2026
% Result : Unsatisfiable 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 18 unt; 0 nHn; 20 RR)
% Number of literals : 44 ( 12 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_right_cancellation,hypothesis,
( X4 = X2
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(another_right_identity,hypothesis,
( product(X1,another_identity,X1)
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_identity) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(another_right_inverse,hypothesis,
( product(X1,another_inverse(X1),another_identity)
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_inverse) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(product_left_cancellation,hypothesis,
( X4 = X1
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(prove_two_inverses_are_equal,negated_conjecture,
inverse(a) != another_inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_inverses_are_equal) ).
cnf(c_0_9,hypothesis,
( X4 = X2
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_10,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_11,hypothesis,
( product(X1,another_identity,X1)
| ~ subgroup_member(X1) ),
another_right_identity ).
cnf(c_0_12,hypothesis,
subgroup_member(a),
a_is_in_subgroup ).
cnf(c_0_13,hypothesis,
( X1 = identity
| ~ product(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,hypothesis,
product(a,another_identity,a),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_16,hypothesis,
identity = another_identity,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,hypothesis,
( product(X1,another_inverse(X1),another_identity)
| ~ subgroup_member(X1) ),
another_right_inverse ).
cnf(c_0_18,plain,
product(inverse(X1),X1,another_identity),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_20,hypothesis,
( X4 = X1
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_21,hypothesis,
product(a,another_inverse(a),another_identity),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_22,hypothesis,
( X1 = X2
| ~ product(inverse(X2),X1,another_identity) ),
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
cnf(c_0_23,plain,
product(X1,inverse(X1),another_identity),
inference(rw,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_24,hypothesis,
( X1 = a
| ~ product(X1,another_inverse(a),another_identity) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,hypothesis,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,hypothesis,
inverse(another_inverse(a)) = a,
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
inverse(a) != another_inverse(a),
prove_two_inverses_are_equal ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP037-3 : TPTP v9.2.1. Released v1.0.0.
% 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 : n028.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 18:18:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------