%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP543-1 : TPTP v9.2.1. Released v2.6.0.
% 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 : n024.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 04:26:21 PM UTC 2026
% Result : Unsatisfiable 1.13s 1.61s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 6 RR)
% Number of literals : 43 ( 42 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(X1) = divide(identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(single_axiom,axiom,
divide(divide(identity,divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_5,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_6,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_7,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_8,axiom,
divide(divide(identity,divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
single_axiom ).
cnf(c_0_9,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_10,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_11,plain,
divide(inverse(divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
inference(rw,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_12,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_13,plain,
multiply(inverse(X1),X1) = identity,
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_14,plain,
divide(X1,identity) = multiply(X1,identity),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
divide(inverse(divide(inverse(X1),X2)),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_7]),c_0_6]) ).
cnf(c_0_16,plain,
divide(multiply(identity,X1),divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_7]),c_0_6]),c_0_12]) ).
cnf(c_0_17,plain,
multiply(identity,identity) = identity,
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_18,plain,
multiply(multiply(identity,X1),identity) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_10]),c_0_6]),c_0_12]) ).
cnf(c_0_19,plain,
multiply(identity,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_6]),c_0_17]),c_0_6]),c_0_12]) ).
cnf(c_0_20,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_22,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_23,plain,
divide(X1,multiply(X1,X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_21,c_0_9]) ).
cnf(c_0_24,plain,
inverse(divide(divide(X1,X2),X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_22]),c_0_14]),c_0_20]) ).
cnf(c_0_25,plain,
multiply(inverse(X1),X2) = divide(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_23]),c_0_12]),c_0_19]) ).
cnf(c_0_26,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_27,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_28,plain,
divide(X1,multiply(identity,X2)) = multiply(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_29,plain,
multiply(inverse(divide(multiply(divide(X1,X2),X3),X1)),X3) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_11]),c_0_9]) ).
cnf(c_0_30,plain,
divide(X1,divide(X2,X3)) = multiply(divide(X3,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_9]) ).
cnf(c_0_32,plain,
divide(multiply(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_26]),c_0_9]) ).
cnf(c_0_33,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(rw,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_34,plain,
multiply(X1,divide(X2,multiply(divide(X2,X3),X1))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_25]),c_0_30]),c_0_31]) ).
cnf(c_0_35,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_32]),c_0_33]),c_0_31]) ).
cnf(c_0_36,plain,
divide(multiply(divide(X1,X2),X3),X1) = divide(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_34]),c_0_26]) ).
cnf(c_0_37,plain,
multiply(divide(X1,X2),X3) = multiply(X1,divide(X3,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
prove_these_axioms_3 ).
cnf(c_0_39,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_9]),c_0_9]) ).
cnf(c_0_40,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[c_0_38,c_0_31]) ).
cnf(c_0_41,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_31,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP543-1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 13:42:26 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.13/1.61 % Version : CSE_E---1.7
% 1.13/1.61 % Problem : theBenchmark.p
% 1.13/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 1.13/1.61 % SZS output start CNFRefutation
% See solution above
% 1.13/1.61 % Total time : 1.361s
%------------------------------------------------------------------------------