%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO002-2 : TPTP v9.2.1. Released v1.1.0.
% 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 : n029.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 04:11:02 PM UTC 2026
% Result : Unsatisfiable 1.69s 1.86s
% Output : CNFRefutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 3 RR)
% Number of literals : 29 ( 28 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 80 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5)) = multiply(X1,X2,multiply(X3,X4,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(ternary_multiply_1,axiom,
multiply(X1,X2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_1) ).
cnf(ternary_multiply_2,axiom,
multiply(X1,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_2) ).
cnf(extra_lemma,axiom,
multiply(X1,X2,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extra_lemma) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(prove_equation,negated_conjecture,
multiply(a,inverse(a),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_6,axiom,
multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5)) = multiply(X1,X2,multiply(X3,X4,X5)),
associativity ).
cnf(c_0_7,axiom,
multiply(X1,X2,X2) = X2,
ternary_multiply_1 ).
cnf(c_0_8,axiom,
multiply(X1,X1,X2) = X1,
ternary_multiply_2 ).
cnf(c_0_9,plain,
multiply(multiply(X1,X2,X3),X4,X2) = multiply(X1,X2,multiply(X3,X4,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,axiom,
multiply(X1,X2,X1) = X1,
extra_lemma ).
cnf(c_0_11,plain,
multiply(X1,X2,multiply(X3,multiply(X1,X2,X3),X4)) = multiply(X1,X2,X3),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_12,plain,
multiply(X1,X2,multiply(X1,X3,X2)) = multiply(X1,X3,X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
multiply(X1,X2,multiply(X3,X1,X4)) = multiply(X3,X1,multiply(X1,X2,X4)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_14,plain,
multiply(X1,X2,multiply(X3,X4,multiply(X1,X2,X3))) = multiply(X1,X2,X3),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
multiply(X1,X2,multiply(X3,X1,X2)) = multiply(X3,X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_7]) ).
cnf(c_0_16,plain,
multiply(multiply(X1,X2,X3),X4,X1) = multiply(X1,X2,multiply(X3,X4,X1)),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_17,plain,
multiply(X1,multiply(X2,X3,X1),X2) = multiply(X2,X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_11]),c_0_7]) ).
cnf(c_0_18,plain,
multiply(X1,X2,multiply(X3,X4,multiply(X1,X2,X4))) = multiply(X1,X2,X4),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_19,plain,
multiply(X1,multiply(X2,X3,X1),multiply(X2,X4,X1)) = multiply(multiply(X2,X3,X1),X4,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
multiply(inverse(X1),X1,X2) = X2,
left_inverse ).
cnf(c_0_21,plain,
multiply(X1,multiply(X2,X3,X1),X3) = multiply(X2,X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_7]) ).
cnf(c_0_22,plain,
multiply(multiply(inverse(X1),X2,X3),X1,X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_10]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(X2,X1,X3),X3) = multiply(X2,X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_24,plain,
multiply(multiply(X1,inverse(X2),X3),X2,X3) = X3,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
multiply(multiply(X1,X2,X3),X1,X3) = multiply(X1,X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_8]),c_0_17]) ).
cnf(c_0_26,negated_conjecture,
multiply(a,inverse(a),b) != b,
prove_equation ).
cnf(c_0_27,plain,
multiply(X1,inverse(X1),X2) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO002-2 : TPTP v9.2.1. Released v1.1.0.
% 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 : n029.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 : Tue May 5 10:44:44 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.69/1.86 % Version : CSE_E---1.7
% 1.69/1.86 % Problem : theBenchmark.p
% 1.69/1.86 % SZS status Unsatisfiable for theBenchmark.p
% 1.69/1.86 % SZS output start CNFRefutation
% See solution above
% 1.69/1.87 % Total time : 1.369s
%------------------------------------------------------------------------------