%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO035-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n002.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 04:11:21 PM UTC 2026
% Result : Unsatisfiable 1.38s 1.80s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of clauses : 33 ( 27 unt; 0 nHn; 8 RR)
% Number of literals : 49 ( 48 equ; 23 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 103 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_tba_axioms,negated_conjecture,
( multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c))
| multiply(b,a,a) != a
| multiply(a,b,inverse(b)) != a
| multiply(a,a,b) != a
| multiply(inverse(b),b,a) != a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_tba_axioms) ).
cnf(c_0_2,axiom,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3)) = X2,
single_axiom ).
cnf(c_0_3,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,X4,multiply(X5,multiply(X6,X7,X8),X9)),inverse(multiply(multiply(X9,X5,X8),X7,multiply(X9,X5,X6))),multiply(X3,X4,multiply(X10,inverse(X10),X11)))),multiply(X4,X11,X3)) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(multiply(X1,X2,X3),inverse(multiply(multiply(X4,X5,X6),X7,multiply(X4,X5,X8))),multiply(X5,multiply(X8,X7,X6),X4)) = multiply(X2,multiply(X3,inverse(multiply(X1,X2,X9)),X9),X1),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_5,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(X3,inverse(X3),multiply(X4,inverse(X4),X5))),multiply(inverse(X3),X5,X3)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_3]),c_0_2]) ).
cnf(c_0_6,plain,
multiply(inverse(X1),multiply(X2,inverse(multiply(X1,inverse(X1),X3)),X3),X1) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_7,plain,
multiply(inverse(X1),X2,X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_5]),c_0_2]) ).
cnf(c_0_8,plain,
multiply(X1,inverse(multiply(X2,inverse(X2),X3)),X3) = X1,
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
inverse(multiply(X1,inverse(X1),X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
multiply(X1,inverse(X2),X2) = X1,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
multiply(X1,inverse(X1),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_7]),c_0_9]),c_0_9]),c_0_10]) ).
cnf(c_0_12,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_13,negated_conjecture,
( multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c))
| multiply(b,a,a) != a
| multiply(a,b,inverse(b)) != a
| multiply(a,a,b) != a
| multiply(inverse(b),b,a) != a ),
prove_tba_axioms ).
cnf(c_0_14,plain,
multiply(inverse(X1),X1,X2) = X2,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
multiply(multiply(X1,X2,X3),inverse(multiply(X4,X5,X6)),multiply(multiply(X4,X5,X6),inverse(multiply(multiply(X7,X8,X9),X10,multiply(X7,X8,X11))),multiply(X8,multiply(X11,X10,X9),X7))) = multiply(X2,multiply(X3,inverse(multiply(X1,X2,X12)),X12),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_4]),c_0_11]) ).
cnf(c_0_16,plain,
multiply(X1,inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
inference(rw,[status(thm)],[c_0_2,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c))
| multiply(a,b,inverse(b)) != a
| multiply(a,a,b) != a
| multiply(b,a,a) != a ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
cnf(c_0_18,plain,
multiply(X1,X2,inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_19,plain,
multiply(X1,multiply(X2,inverse(multiply(X3,X1,X4)),X4),X3) = multiply(X3,X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_10]) ).
cnf(c_0_20,negated_conjecture,
( multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c))
| multiply(a,a,b) != a
| multiply(b,a,a) != a ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_21,plain,
multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5)) = multiply(X2,multiply(X5,X4,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_12]) ).
cnf(c_0_22,plain,
multiply(X1,X2,inverse(X1)) = X2,
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_23,plain,
multiply(X1,X2,multiply(X1,X2,X3)) = multiply(X2,X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_12]) ).
cnf(c_0_24,negated_conjecture,
( multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c))
| multiply(a,a,b) != a
| multiply(b,a,a) != a ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
multiply(X1,X2,X3) = multiply(X3,X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_14]),c_0_22]) ).
cnf(c_0_26,plain,
multiply(X1,X2,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_10]) ).
cnf(c_0_27,negated_conjecture,
( multiply(d,multiply(a,b,c),e) != multiply(d,e,multiply(a,b,c))
| multiply(a,a,b) != a ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25]),c_0_25])]) ).
cnf(c_0_28,plain,
multiply(X1,X1,X2) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
multiply(X1,X2,X3) = multiply(X3,X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_26]),c_0_10]) ).
cnf(c_0_30,negated_conjecture,
multiply(d,multiply(a,b,c),e) != multiply(d,e,multiply(a,b,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_31,plain,
multiply(X1,X2,X3) = multiply(X1,X3,X2),
inference(spm,[status(thm)],[c_0_25,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO035-1 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.13/0.32 % Computer : n002.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 10:45:03 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.38/1.80 % Version : CSE_E---1.7
% 1.38/1.80 % Problem : theBenchmark.p
% 1.38/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 1.38/1.80 % SZS output start CNFRefutation
% See solution above
% 1.48/1.80 % Total time : 1.370s
%------------------------------------------------------------------------------