%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG038-1 : 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 : n018.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 08:25:40 AM UTC 2026
% Result : Unsatisfiable 29.12s 3.99s
% Output : CNFRefutation 29.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 63 ( 31 unt; 0 nHn; 39 RR)
% Number of literals : 124 ( 22 equ; 64 neg)
% Maximal clause size : 5 ( 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; 3 con; 0-2 aty)
% Number of variables : 154 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(some_property,hypothesis,
( product(X0,h(X0,X1),X1)
| X0 != 'additive$uidentity' ) ).
cnf(a_times_b,hypothesis,
product(a,b,'additive$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$uidentity',X0) ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) ).
cnf(left_inverse,axiom,
sum('additive$uinverse'(X0),X0,'additive$uidentity') ).
cnf(right_inverse,axiom,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') ).
cnf(associativity_of_addition1,axiom,
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(associativity_of_addition2,axiom,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(commutativity_of_addition,axiom,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(associativity_of_multiplication1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
( product(X0,h(X0,X1),X1)
| X0 != 'additive$uidentity' ),
inference(clausification,[status(esa)],[some_property]) ).
cnf(c1,plain,
product(a,b,'additive$uidentity'),
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c3,plain,
b != 'additive$uidentity',
inference(clausification,[status(esa)],[prove_b_is_additive_identity]) ).
cnf(c4,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c5,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c6,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c7,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c8,plain,
sum('additive$uinverse'(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c9,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c10,plain,
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_addition1]) ).
cnf(c11,plain,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_addition2]) ).
cnf(c12,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c13,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(c15,plain,
( ~ product(X0,X6,X3)
| ~ sum(X6,X5,X1)
| ~ product(X0,X5,X4)
| sum(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c19,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c20,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ product(a,b,X0)
| 'additive$uidentity' = X0 ),
inference(resolution,[status(thm)],[c20,c1]) ).
cnf(d1,plain,
product('additive$uidentity',h('additive$uidentity',X0),X0),
inference(equality_resolution,[status(thm)],[c0]) ).
cnf(d2,plain,
( ~ product(X3,X0,'additive$uidentity')
| product(X3,X2,X1)
| ~ product(X0,h('additive$uidentity',X1),X2) ),
inference(resolution,[status(thm)],[c13,d1]) ).
cnf(d3,plain,
( ~ product(X0,'additive$uidentity','additive$uidentity')
| product(X0,X1,X1) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c12,c7]) ).
cnf(d5,plain,
( ~ sum(X1,'additive$uidentity',X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c19,c5]) ).
cnf(d6,plain,
add('additive$uidentity',X0) = X0,
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ sum(X4,X3,X1)
| ~ sum(X0,X4,X2)
| sum(X0,X1,add(X2,X3)) ),
inference(resolution,[status(thm)],[c10,c7]) ).
cnf(d8,plain,
( sum(X0,X2,add('additive$uidentity',X1))
| ~ sum('additive$uinverse'(X0),X1,X2) ),
inference(resolution,[status(thm)],[d7,c9]) ).
cnf(d9,plain,
( ~ sum('additive$uinverse'(X1),X0,X2)
| sum(X1,X2,X0) ),
inference(demodulation,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
sum(X0,add('additive$uinverse'(X0),X1),X1),
inference(resolution,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
sum(add('additive$uinverse'(X0),X1),X0,X1),
inference(resolution,[status(thm)],[d10,c12]) ).
cnf(d12,plain,
( ~ sum('additive$uinverse'(X3),X2,X0)
| ~ sum(X2,X1,X3)
| sum(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[c11,c8]) ).
cnf(d13,plain,
( sum(add('additive$uinverse'(X2),X0),X1,'additive$uidentity')
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d12,c7]) ).
cnf(d14,plain,
( ~ sum(add('additive$uinverse'(X2),X0),X1,X3)
| X3 = 'additive$uidentity'
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d13,c19]) ).
cnf(d15,plain,
( ~ sum(X0,X1,X1)
| X0 = 'additive$uidentity' ),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( sum(X2,X3,X4)
| ~ product(X0,X1,X4)
| ~ product(X0,'additive$uidentity',X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c5]) ).
cnf(d17,plain,
( sum(X3,multiply(X0,'additive$uidentity'),X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d16,c6]) ).
cnf(d18,plain,
( sum(X2,multiply(X0,'additive$uidentity'),multiply(X0,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d17,c6]) ).
cnf(d19,plain,
( X1 = 'additive$uidentity'
| ~ product(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
multiply(X0,'additive$uidentity') = 'additive$uidentity',
inference(resolution,[status(thm)],[d19,c6]) ).
cnf(d21,plain,
product(X0,'additive$uidentity','additive$uidentity'),
inference(superposition,[status(thm)],[d20,c6]) ).
cnf(d22,plain,
product(X0,X1,X1),
inference(resolution,[status(thm)],[d21,d3]) ).
cnf(d23,plain,
'additive$uidentity' = b,
inference(resolution,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
'additive$uidentity' != 'additive$uidentity',
inference(demodulation,[status(thm)],[c3,d23]) ).
cnf(d25,plain,
( ~ sum(X1,'additive$uinverse'(X1),X0)
| X0 = 'additive$uidentity' ),
inference(resolution,[status(thm)],[c19,c9]) ).
cnf(d26,plain,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity',
inference(resolution,[status(thm)],[d25,c7]) ).
cnf(d27,plain,
'additive$uinverse'('additive$uidentity') = 'additive$uidentity',
inference(resolution,[status(thm)],[d25,c4]) ).
cnf(d28,plain,
add('additive$uidentity','additive$uidentity') = 'additive$uidentity',
inference(superposition,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
'additive$uidentity' = 'additive$uidentity',
inference(demodulation,[status(thm)],[d28,d6]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d29,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 05:53:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.12/3.99 % SZS status Unsatisfiable for theBenchmark.p
% 29.12/3.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------