%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP122-1 : 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 : n010.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 1.57s 1.81s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 5 RR)
% Number of literals : 60 ( 59 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 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_order3,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_order3) ).
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,multiply(X2,multiply(X2,X2))),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_38]),c_0_38]),c_0_43]) ).
cnf(c_0_45,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_46,plain,
multiply(multiply(X1,multiply(X1,multiply(X2,multiply(X2,X2)))),X2) = multiply(X1,X1),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_47,plain,
multiply(multiply(multiply(X1,X2),X1),X2) = multiply(multiply(X1,X2),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_46,c_0_44]),c_0_20]),c_0_43]),c_0_20]),c_0_43]),c_0_20]),c_0_43]) ).
cnf(c_0_48,plain,
multiply(multiply(X1,multiply(X1,X1)),X1) = identity,
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_49,plain,
multiply(X1,multiply(X1,multiply(X1,X1))) = identity,
inference(rw,[status(thm)],[c_0_42,c_0_45]) ).
cnf(c_0_50,plain,
multiply(multiply(X1,multiply(X1,multiply(X1,multiply(X2,X3)))),multiply(X3,multiply(X3,X3))) = multiply(X1,multiply(X1,multiply(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_38]),c_0_38]),c_0_45]),c_0_45]) ).
cnf(c_0_51,plain,
multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))) = multiply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_43]) ).
cnf(c_0_52,plain,
multiply(multiply(X1,multiply(X2,X2)),multiply(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_49]),c_0_45]),c_0_38]) ).
cnf(c_0_53,plain,
multiply(multiply(X1,multiply(X1,X1)),X2) = multiply(X1,multiply(X1,multiply(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_49]),c_0_38]),c_0_20]),c_0_43]) ).
cnf(c_0_54,plain,
multiply(X1,multiply(X1,multiply(X1,multiply(X1,X2)))) = X2,
inference(rw,[status(thm)],[c_0_40,c_0_45]) ).
cnf(c_0_55,plain,
multiply(multiply(X1,X2),multiply(X2,multiply(X2,X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_51]),c_0_52]) ).
cnf(c_0_56,plain,
multiply(multiply(X1,multiply(X2,X3)),multiply(X3,multiply(X3,X3))) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_53]),c_0_53]),c_0_53]),c_0_54]),c_0_54]),c_0_53]),c_0_53]),c_0_54]),c_0_53]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
prove_order3 ).
cnf(c_0_58,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_20]),c_0_43]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP122-1 : 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 : n010.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 18:23:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.57/1.81 % Version : CSE_E---1.7
% 1.57/1.81 % Problem : theBenchmark.p
% 1.57/1.81 % SZS status Unsatisfiable for theBenchmark.p
% 1.57/1.81 % SZS output start CNFRefutation
% See solution above
% 1.57/1.81 % Total time : 1.371s
%------------------------------------------------------------------------------