%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO029-1 : 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 : n021.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 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 3 RR)
% Number of literals : 22 ( 21 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 45 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(l1,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
cnf(l2,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).
cnf(associativity_of_add,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(b2,axiom,
add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(prove_equal_inverse,negated_conjecture,
add(b,inverse(b)) != add(a,inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_inverse) ).
cnf(c_0_6,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
l1 ).
cnf(c_0_7,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
l2 ).
cnf(c_0_8,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_9,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
add(X1,add(multiply(X2,X1),X3)) = add(X1,X3),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,axiom,
add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
b2 ).
cnf(c_0_12,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_14,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
multiply(X1,add(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_16,plain,
add(X1,add(X2,inverse(X1))) = add(X1,inverse(X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
multiply(X1,add(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_18,plain,
multiply(add(X1,inverse(X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
add(b,inverse(b)) != add(a,inverse(a)),
prove_equal_inverse ).
cnf(c_0_20,plain,
add(X1,inverse(X1)) = add(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_18]),c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_19,c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO029-1 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n021.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 10:45:42 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------