%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 16.05s 7.45s
% Output : CNFRefutation 16.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of clauses : 69 ( 55 unt; 0 nHn; 36 RR)
% Number of literals : 87 ( 36 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 69 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(absorbtion2,axiom,
sum(add(X0,X1),X1,X0) ).
cnf(clause34,axiom,
add(X0,X0) = 'additive$uidentity' ).
cnf(clause35,axiom,
multiply(X0,X0) = X0 ).
cnf(clause37,axiom,
multiply(b,a) = d ).
cnf(clause44,axiom,
product(a,multiply(b,X0),multiply(X1,X0)) ).
cnf(clause57,axiom,
product(multiply(X0,b),a,multiply(X0,d)) ).
cnf(clause68,axiom,
product(add(b,a),b,add(b,c)) ).
cnf(clause69,axiom,
product(add(b,a),a,add(d,a)) ).
cnf(a_times_b,negated_conjecture,
product(a,b,c) ).
cnf(b_times_a,negated_conjecture,
product(b,a,d) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) ).
cnf(right_inverse,axiom,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') ).
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(c1,plain,
sum(add(X0,X1),X1,X0),
inference(clausification,[status(esa)],[absorbtion2]) ).
cnf(c4,plain,
add(X0,X0) = 'additive$uidentity',
inference(clausification,[status(esa)],[clause34]) ).
cnf(c5,plain,
multiply(X0,X0) = X0,
inference(clausification,[status(esa)],[clause35]) ).
cnf(c7,plain,
multiply(b,a) = d,
inference(clausification,[status(esa)],[clause37]) ).
cnf(c14,plain,
product(a,multiply(b,X0),multiply(X1,X0)),
inference(clausification,[status(esa)],[clause44]) ).
cnf(c27,plain,
product(multiply(X0,b),a,multiply(X0,d)),
inference(clausification,[status(esa)],[clause57]) ).
cnf(c36,plain,
product(add(b,a),b,add(b,c)),
inference(clausification,[status(esa)],[clause68]) ).
cnf(c37,plain,
product(add(b,a),a,add(d,a)),
inference(clausification,[status(esa)],[clause69]) ).
cnf(c40,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c41,plain,
product(b,a,d),
inference(clausification,[status(esa)],[b_times_a]) ).
cnf(c42,plain,
c != d,
inference(clausification,[status(esa)],[prove_c_equals_d]) ).
cnf(c43,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c45,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c46,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c48,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c58,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c59,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,multiply(X0,b)),
inference(superposition,[status(thm)],[c5,c14]) ).
cnf(d1,plain,
product(a,b,b),
inference(superposition,[status(thm)],[c5,d0]) ).
cnf(d2,plain,
( ~ product(a,b,X0)
| c = X0 ),
inference(resolution,[status(thm)],[c59,c40]) ).
cnf(d3,plain,
c = b,
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
c = multiply(X0,b),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d5,plain,
b = multiply(X0,b),
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
product(X0,b,b),
inference(superposition,[status(thm)],[d5,c45]) ).
cnf(d7,plain,
( ~ product(add(b,a),b,X0)
| add(b,c) = X0 ),
inference(resolution,[status(thm)],[c59,c36]) ).
cnf(d8,plain,
( ~ product(add(b,a),b,X0)
| add(b,b) = X0 ),
inference(demodulation,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( ~ product(add(b,a),b,X0)
| 'additive$uidentity' = X0 ),
inference(demodulation,[status(thm)],[d8,c4]) ).
cnf(d10,plain,
'additive$uidentity' = b,
inference(resolution,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( ~ sum('additive$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c58,c43]) ).
cnf(d12,plain,
( ~ sum(X1,'additive$uinverse'(X1),X0)
| X0 = 'additive$uidentity' ),
inference(resolution,[status(thm)],[c58,c48]) ).
cnf(d13,plain,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity',
inference(resolution,[status(thm)],[d12,c46]) ).
cnf(d14,plain,
sum('additive$uidentity','additive$uinverse'(X0),X0),
inference(superposition,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
X0 = 'additive$uinverse'(X0),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
add(X0,X0) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d13,d15]) ).
cnf(d17,plain,
add(X0,X0) = b,
inference(demodulation,[status(thm)],[d16,d10]) ).
cnf(d18,plain,
( ~ product(b,a,X0)
| d = X0 ),
inference(resolution,[status(thm)],[c59,c41]) ).
cnf(d19,plain,
product(b,a,multiply(X0,d)),
inference(demodulation,[status(thm)],[c27,d5]) ).
cnf(d20,plain,
d = multiply(X0,d),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
product(X0,d,d),
inference(superposition,[status(thm)],[d20,c45]) ).
cnf(d22,plain,
product(a,d,multiply(X0,a)),
inference(superposition,[status(thm)],[c7,c14]) ).
cnf(d23,plain,
product(a,d,a),
inference(superposition,[status(thm)],[c5,d22]) ).
cnf(d24,plain,
( ~ product(a,d,X0)
| a = X0 ),
inference(resolution,[status(thm)],[d23,c59]) ).
cnf(d25,plain,
a = d,
inference(resolution,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
product(X0,a,d),
inference(demodulation,[status(thm)],[d21,d25]) ).
cnf(d27,plain,
product(X0,a,a),
inference(demodulation,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
( ~ product(add(b,a),a,X0)
| add(d,a) = X0 ),
inference(resolution,[status(thm)],[c59,c37]) ).
cnf(d29,plain,
( ~ product(add(b,a),a,X0)
| add(a,a) = X0 ),
inference(demodulation,[status(thm)],[d28,d25]) ).
cnf(d30,plain,
add(a,a) = a,
inference(resolution,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
b = a,
inference(demodulation,[status(thm)],[d30,d17]) ).
cnf(d32,plain,
b != d,
inference(demodulation,[status(thm)],[c42,d3]) ).
cnf(d33,plain,
b != a,
inference(demodulation,[status(thm)],[d32,d25]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[d33,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n014.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 26 05:50:55 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.05/7.45 % SZS status Unsatisfiable for theBenchmark.p
% 16.05/7.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------