%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG041-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : n009.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 05:05:06 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 15 unt; 2 nHn; 16 RR)
% Number of literals : 42 ( 11 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(multiplicative_identity2,hypothesis,
product(X1,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
cnf(associativity_of_multiplication2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
cnf(a_times_b,negated_conjecture,
product(a,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(left_multiplicative_identity,hypothesis,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_identity) ).
cnf(clause42,hypothesis,
( product(h(X1),X1,multiplicative_identity)
| X1 = additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
cnf(a_not_additive_identity,negated_conjecture,
a != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_additive_identity) ).
cnf(prove_b_is_additive_identity,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
cnf(c_0_9,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_10,hypothesis,
product(X1,additive_identity,additive_identity),
multiplicative_identity2 ).
cnf(c_0_11,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2 ).
cnf(c_0_12,negated_conjecture,
product(a,b,additive_identity),
a_times_b ).
cnf(c_0_13,hypothesis,
( X1 = additive_identity
| ~ product(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_15,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,additive_identity,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,hypothesis,
product(multiplicative_identity,X1,X1),
left_multiplicative_identity ).
cnf(c_0_18,negated_conjecture,
( product(X1,b,additive_identity)
| ~ product(X2,a,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_16]) ).
cnf(c_0_19,hypothesis,
( product(h(X1),X1,multiplicative_identity)
| X1 = additive_identity ),
clause42 ).
cnf(c_0_20,negated_conjecture,
a != additive_identity,
a_not_additive_identity ).
cnf(c_0_21,hypothesis,
( X1 = X2
| ~ product(multiplicative_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_22,hypothesis,
product(multiplicative_identity,b,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
b != additive_identity,
prove_b_is_additive_identity ).
cnf(c_0_24,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG041-1 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.14/0.32 % Computer : n009.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:47:41 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------