%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP525-1 : TPTP v9.2.1. Released v2.6.0.
% 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 : n005.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 04:26:19 PM UTC 2026
% Result : Unsatisfiable 1.27s 1.74s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 5 RR)
% Number of literals : 34 ( 33 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(single_axiom,axiom,
divide(X1,divide(divide(X1,X2),divide(X3,X2))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c_0_4,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_5,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_6,axiom,
divide(X1,divide(divide(X1,X2),divide(X3,X2))) = X3,
single_axiom ).
cnf(c_0_7,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_5]),c_0_7]) ).
cnf(c_0_9,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_11,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
multiply(divide(X1,X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_13,plain,
inverse(multiply(multiply(inverse(X1),X2),X1)) = inverse(X2),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_15,plain,
multiply(inverse(X1),X2) = inverse(divide(X1,X2)),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_16,plain,
inverse(inverse(inverse(X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
inverse(divide(X1,multiply(X2,X1))) = X2,
inference(rw,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_18,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
divide(divide(X1,X2),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_15]),c_0_15]),c_0_18]) ).
cnf(c_0_20,plain,
multiply(divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_19]),c_0_7]) ).
cnf(c_0_21,plain,
divide(multiply(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_7]),c_0_18]) ).
cnf(c_0_22,plain,
multiply(divide(X1,X1),X2) = X2,
inference(rw,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
prove_these_axioms_1 ).
cnf(c_0_24,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_7,c_0_18]) ).
cnf(c_0_26,plain,
inverse(divide(inverse(X1),X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_27,plain,
divide(X1,divide(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
inverse(divide(a1,a1)) != inverse(divide(b1,b1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_15]),c_0_15]) ).
cnf(c_0_29,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_24]),c_0_25]) ).
cnf(c_0_30,plain,
multiply(X1,divide(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_18]) ).
cnf(c_0_31,negated_conjecture,
divide(a1,a1) != divide(b1,b1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]) ).
cnf(c_0_32,plain,
divide(X1,X1) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_31,c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP525-1 : TPTP v9.2.1. Released v2.6.0.
% 0.13/0.13 % 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
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 18:42:15 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.20/0.36 % start to proof: theBenchmark
% 1.27/1.74 % Version : CSE_E---1.7
% 1.27/1.74 % Problem : theBenchmark.p
% 1.27/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.74 % SZS output start CNFRefutation
% See solution above
% 1.27/1.74 % Total time : 1.375s
%------------------------------------------------------------------------------