%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG041-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:25:41 AM UTC 2026
% Result : Unsatisfiable 9.45s 2.93s
% Output : CNFRefutation 9.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 44 ( 28 unt; 3 nHn; 27 RR)
% Number of literals : 70 ( 21 equ; 28 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiplicative_identity1,hypothesis,
product('additive$uidentity',X0,'additive$uidentity') ).
cnf(right_multiplicative_identity,hypothesis,
product(X0,'multiplicative$uidentity',X0) ).
cnf(clause41,hypothesis,
( X0 = 'additive$uidentity'
| product(X0,h(X0),'multiplicative$uidentity') ) ).
cnf(a_times_b,negated_conjecture,
product(a,b,'additive$uidentity') ).
cnf(a_not_additive_identity,negated_conjecture,
a != 'additive$uidentity' ).
cnf(prove_b_is_additive_identity,negated_conjecture,
b != 'additive$uidentity' ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) ).
cnf(right_inverse,axiom,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') ).
cnf(commutativity_of_addition,axiom,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(associativity_of_multiplication1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
product('additive$uidentity',X0,'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_identity1]) ).
cnf(c2,plain,
product(X0,'multiplicative$uidentity',X0),
inference(clausification,[status(esa)],[right_multiplicative_identity]) ).
cnf(c4,plain,
( X0 = 'additive$uidentity'
| product(X0,h(X0),'multiplicative$uidentity') ),
inference(clausification,[status(esa)],[clause41]) ).
cnf(c6,plain,
product(a,b,'additive$uidentity'),
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c7,plain,
a != 'additive$uidentity',
inference(clausification,[status(esa)],[a_not_additive_identity]) ).
cnf(c8,plain,
b != 'additive$uidentity',
inference(clausification,[status(esa)],[prove_b_is_additive_identity]) ).
cnf(c9,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c10,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c12,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c14,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c17,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c18,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_multiplication1]) ).
cnf(c24,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c25,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ product(X1,'multiplicative$uidentity',X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c25,c2]) ).
cnf(d1,plain,
( product(a,X2,X1)
| ~ product(b,X0,X2)
| ~ product('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c18,c6]) ).
cnf(d2,plain,
( b = 'additive$uidentity'
| product(a,'multiplicative$uidentity',X0)
| ~ product('additive$uidentity',h(b),X0) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( product(a,'multiplicative$uidentity',X0)
| ~ product('additive$uidentity',h(b),X0) ),
inference(resolution,[status(thm)],[c8,d2]) ).
cnf(d4,plain,
product(a,'multiplicative$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
'additive$uidentity' = a,
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
'additive$uidentity' != 'additive$uidentity',
inference(demodulation,[status(thm)],[c7,d5]) ).
cnf(d7,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c17,c12]) ).
cnf(d8,plain,
( ~ sum(X1,'additive$uidentity',X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c24,c10]) ).
cnf(d9,plain,
add('additive$uidentity',X0) = X0,
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ sum(X1,'additive$uinverse'(X1),X0)
| X0 = 'additive$uidentity' ),
inference(resolution,[status(thm)],[c24,c14]) ).
cnf(d11,plain,
add('additive$uinverse'(X0),X0) = 'additive$uidentity',
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
'additive$uinverse'('additive$uidentity') = 'additive$uidentity',
inference(resolution,[status(thm)],[d10,c9]) ).
cnf(d13,plain,
add('additive$uidentity','additive$uidentity') = 'additive$uidentity',
inference(superposition,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
'additive$uidentity' = 'additive$uidentity',
inference(demodulation,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG041-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 05:51:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.45/2.93 % SZS status Unsatisfiable for theBenchmark.p
% 9.45/2.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------