%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP119-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n013.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 04:23:53 PM UTC 2026
% Result : Unsatisfiable 1.34s 1.76s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 5 RR)
% Number of literals : 48 ( 47 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X1),multiply(X2,X3))),multiply(X3,multiply(X3,X3)))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(single_axiom2,axiom,
multiply(identity,identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom2) ).
cnf(prove_order4,negated_conjecture,
multiply(a,multiply(a,multiply(a,a))) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_order4) ).
cnf(c_0_3,axiom,
multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X1),multiply(X2,X3))),multiply(X3,multiply(X3,X3)))) = X2,
single_axiom ).
cnf(c_0_4,axiom,
multiply(identity,identity) = identity,
single_axiom2 ).
cnf(c_0_5,plain,
multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X1),multiply(X2,identity))),identity)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_4]) ).
cnf(c_0_6,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X1,identity))),identity)) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_7,plain,
multiply(multiply(X1,X1),multiply(multiply(multiply(X1,X1),multiply(X1,X1)),multiply(X2,identity))) = multiply(X1,multiply(multiply(X1,X2),identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_4]),c_0_4]) ).
cnf(c_0_8,plain,
multiply(identity,multiply(multiply(identity,X1),identity)) = multiply(identity,multiply(identity,multiply(X1,identity))),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_9,plain,
multiply(multiply(X1,X1),multiply(multiply(X1,multiply(multiply(X1,X2),identity)),identity)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_7]),c_0_4]),c_0_4]) ).
cnf(c_0_10,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X1,X2))),multiply(X2,multiply(X2,X2)))) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_11,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X1,identity),identity)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X1),identity)),identity)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_4]),c_0_4]) ).
cnf(c_0_13,plain,
multiply(multiply(identity,multiply(identity,multiply(X1,X2))),multiply(X2,multiply(X2,X2))) = multiply(identity,multiply(identity,multiply(multiply(X1,identity),identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_4]),c_0_8]) ).
cnf(c_0_14,plain,
multiply(multiply(identity,X1),identity) = multiply(identity,multiply(X1,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_8]),c_0_4]),c_0_8]),c_0_8]),c_0_11]) ).
cnf(c_0_15,plain,
multiply(multiply(X1,X1),multiply(multiply(multiply(X1,X1),multiply(X1,X1)),identity)) = multiply(X1,multiply(multiply(X1,identity),identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_12]),c_0_4]),c_0_4]) ).
cnf(c_0_16,plain,
multiply(multiply(identity,X1),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_13]),c_0_11]),c_0_14]),c_0_14]),c_0_14]),c_0_14]),c_0_11]) ).
cnf(c_0_17,plain,
multiply(X1,multiply(multiply(X1,multiply(X1,multiply(multiply(X1,identity),identity))),identity)) = multiply(multiply(X1,X1),multiply(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_15]),c_0_4]),c_0_4]) ).
cnf(c_0_18,plain,
multiply(identity,multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))))) = multiply(identity,multiply(identity,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]) ).
cnf(c_0_19,plain,
multiply(multiply(X1,multiply(multiply(X1,X1),multiply(X2,X3))),multiply(X3,multiply(X3,X3))) = multiply(multiply(X1,X1),multiply(multiply(X1,multiply(X2,identity)),identity)),
inference(spm,[status(thm)],[c_0_9,c_0_3]) ).
cnf(c_0_20,plain,
multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1)))) = multiply(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_18]),c_0_4]),c_0_14]),c_0_14]),c_0_14]),c_0_8]),c_0_8]),c_0_11]) ).
cnf(c_0_21,plain,
multiply(identity,multiply(multiply(identity,multiply(X1,multiply(X2,multiply(X2,X2)))),X2)) = multiply(identity,multiply(identity,multiply(multiply(X1,identity),identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_4]),c_0_4]),c_0_14]) ).
cnf(c_0_22,plain,
multiply(multiply(identity,X1),multiply(identity,X2)) = multiply(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_23,plain,
multiply(multiply(identity,multiply(X1,multiply(X2,multiply(X2,X2)))),X2) = multiply(identity,multiply(multiply(X1,identity),identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_21]),c_0_4]),c_0_8]),c_0_8]),c_0_11]) ).
cnf(c_0_24,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(X1,identity),identity))),X2)) = multiply(X1,multiply(identity,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_11]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X1),multiply(identity,multiply(X2,identity)))),identity)) = multiply(identity,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_14]),c_0_4]),c_0_4]) ).
cnf(c_0_26,plain,
multiply(multiply(X1,multiply(identity,multiply(X2,multiply(X2,X2)))),X2) = multiply(multiply(X1,identity),identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14]),c_0_8]),c_0_14]),c_0_14]),c_0_11]) ).
cnf(c_0_27,plain,
multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X1),X2)),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(X2,identity)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_5]),c_0_4]) ).
cnf(c_0_28,plain,
multiply(multiply(multiply(X1,multiply(identity,multiply(identity,multiply(identity,X2)))),identity),identity) = multiply(multiply(multiply(X1,identity),identity),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_26]),c_0_22]),c_0_22]),c_0_20]) ).
cnf(c_0_29,plain,
multiply(multiply(X1,multiply(multiply(X1,X1),X2)),identity) = multiply(multiply(X1,X1),multiply(multiply(X1,X2),identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_27]),c_0_14]),c_0_14]),c_0_14]),c_0_11]) ).
cnf(c_0_30,plain,
multiply(X1,multiply(multiply(multiply(X1,identity),identity),multiply(multiply(multiply(X1,identity),identity),multiply(multiply(X1,identity),identity)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_4]),c_0_4]),c_0_4]),c_0_4]) ).
cnf(c_0_31,plain,
multiply(multiply(multiply(X1,identity),identity),multiply(multiply(X2,identity),identity)) = multiply(multiply(multiply(X1,X2),identity),identity),
inference(spm,[status(thm)],[c_0_28,c_0_11]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(multiply(X1,X1),multiply(multiply(X1,X2),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(X2,identity)))),
inference(rw,[status(thm)],[c_0_27,c_0_29]) ).
cnf(c_0_33,plain,
multiply(X1,multiply(multiply(multiply(X1,multiply(X1,X1)),identity),identity)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,multiply(X1,X1)),identity) = multiply(X1,multiply(multiply(X1,X1),identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_4]),c_0_11]) ).
cnf(c_0_35,plain,
multiply(X1,multiply(multiply(X1,X1),multiply(X1,multiply(multiply(X1,X1),identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X1,X1),identity)))),
inference(spm,[status(thm)],[c_0_32,c_0_34]) ).
cnf(c_0_36,plain,
multiply(multiply(X1,X1),multiply(multiply(X1,multiply(X1,identity)),identity)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_35]),c_0_13]),c_0_4]),c_0_4]),c_0_4]),c_0_4]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,multiply(multiply(X1,X1),identity)),identity) = multiply(multiply(X1,X1),multiply(multiply(X1,identity),identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_4]) ).
cnf(c_0_38,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_36]),c_0_11]) ).
cnf(c_0_39,plain,
multiply(multiply(X1,X1),multiply(multiply(X1,X1),multiply(multiply(X1,identity),identity))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_37]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,X1),multiply(X1,multiply(X1,X2))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_38]),c_0_38]) ).
cnf(c_0_41,plain,
multiply(multiply(X1,X1),multiply(multiply(X1,X1),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_38]),c_0_38]) ).
cnf(c_0_42,plain,
multiply(multiply(X1,X1),multiply(X1,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_38]),c_0_38]) ).
cnf(c_0_43,plain,
multiply(identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_44,plain,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_40]),c_0_42]),c_0_43]) ).
cnf(c_0_45,negated_conjecture,
multiply(a,multiply(a,multiply(a,a))) != identity,
prove_order4 ).
cnf(c_0_46,plain,
multiply(X1,multiply(X1,multiply(X1,X1))) = identity,
inference(rw,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP119-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:21:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.34/1.76 % Version : CSE_E---1.7
% 1.34/1.76 % Problem : theBenchmark.p
% 1.34/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.34/1.76 % SZS output start CNFRefutation
% See solution above
% 1.34/1.76 % Total time : 1.373s
%------------------------------------------------------------------------------