%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG004-1 : 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 : n004.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 08:25:32 AM UTC 2026
% Result : Unsatisfiable 9.21s 13.56s
% Output : CNFRefutation 9.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of clauses : 96 ( 58 unt; 0 nHn; 73 RR)
% Number of literals : 172 ( 30 equ; 79 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 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 : 174 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_times_b,hypothesis,
product(a,b,c) ).
cnf(a_inverse_times_b_inverse,hypothesis,
product('additive$uinverse'(a),'additive$uinverse'(b),d) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d ).
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(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity3,axiom,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(c0,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c1,plain,
product('additive$uinverse'(a),'additive$uinverse'(b),d),
inference(clausification,[status(esa)],[a_inverse_times_b_inverse]) ).
cnf(c2,plain,
d != c,
inference(clausification,[status(esa)],[prove_c_equals_d]) ).
cnf(c3,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c4,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c5,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c6,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c7,plain,
sum('additive$uinverse'(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c8,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c9,plain,
( sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_addition1]) ).
cnf(c10,plain,
( sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_addition2]) ).
cnf(c11,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c14,plain,
( ~ product(X0,X3,X5)
| ~ product(X0,X4,X6)
| sum(X5,X2,X6)
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c16,plain,
( ~ product(X5,X4,X0)
| ~ product(X6,X4,X2)
| ~ sum(X5,X3,X6)
| ~ product(X3,X4,X1)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c18,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(d0,plain,
( ~ sum('additive$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c18,c3]) ).
cnf(d1,plain,
( ~ sum(X3,'additive$uidentity',X2)
| ~ sum(X3,'additive$uinverse'(X1),X0)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c7]) ).
cnf(d2,plain,
( sum(add(X0,'additive$uinverse'(X2)),X2,X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
sum(add(X0,'additive$uinverse'(X1)),X1,X0),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c11,c6]) ).
cnf(d5,plain,
( ~ sum(X2,X1,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[c18,d4]) ).
cnf(d6,plain,
add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( ~ sum(X1,X2,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[c18,c6]) ).
cnf(d8,plain,
( ~ sum(X1,'additive$uinverse'(X1),X0)
| X0 = 'additive$uidentity' ),
inference(resolution,[status(thm)],[c18,c8]) ).
cnf(d9,plain,
( ~ sum(X3,'additive$uidentity',X2)
| ~ sum(X3,X1,X0)
| sum(X0,'additive$uinverse'(X1),X2) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(d10,plain,
( sum(add(X2,X0),'additive$uinverse'(X2),X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
sum(add(X0,X1),'additive$uinverse'(X0),X1),
inference(resolution,[status(thm)],[d10,c4]) ).
cnf(d12,plain,
( ~ sum(X5,X0,X3)
| sum(multiply(X5,X1),X2,X4)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c16,c5]) ).
cnf(d13,plain,
( sum(multiply(X2,b),X1,c)
| ~ sum(X2,X0,a)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
( sum(multiply(X0,b),c,c)
| ~ sum(X0,a,a) ),
inference(resolution,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
sum(multiply('additive$uidentity',b),c,c),
inference(resolution,[status(thm)],[d14,c3]) ).
cnf(d16,plain,
c = add(multiply('additive$uidentity',b),c),
inference(resolution,[status(thm)],[d15,d7]) ).
cnf(d17,plain,
c = add(c,multiply('additive$uidentity',b)),
inference(demodulation,[status(thm)],[d16,d6]) ).
cnf(d18,plain,
sum(c,'additive$uinverse'(c),multiply('additive$uidentity',b)),
inference(superposition,[status(thm)],[d17,d11]) ).
cnf(d19,plain,
multiply('additive$uidentity',b) = 'additive$uidentity',
inference(resolution,[status(thm)],[d18,d8]) ).
cnf(d20,plain,
( ~ sum(X1,'additive$uidentity',X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c18,c4]) ).
cnf(d21,plain,
( ~ sum('additive$uinverse'(X0),X3,X1)
| ~ sum('additive$uidentity',X3,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c8]) ).
cnf(d22,plain,
( ~ sum('additive$uidentity','additive$uinverse'('additive$uinverse'(X0)),X1)
| sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d21,c8]) ).
cnf(d23,plain,
sum(X0,'additive$uidentity','additive$uinverse'('additive$uinverse'(X0))),
inference(resolution,[status(thm)],[d22,c3]) ).
cnf(d24,plain,
'additive$uinverse'('additive$uinverse'(X0)) = X0,
inference(resolution,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
( sum(add(X0,X2),'additive$uinverse'(X2),X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d9,c6]) ).
cnf(d26,plain,
sum(add(X0,X1),'additive$uinverse'(X1),X0),
inference(resolution,[status(thm)],[d25,c4]) ).
cnf(d27,plain,
( ~ sum(X0,X2,'additive$uinverse'(b))
| sum(X1,X3,d)
| ~ product('additive$uinverse'(a),X2,X3)
| ~ product('additive$uinverse'(a),X0,X1) ),
inference(resolution,[status(thm)],[c14,c1]) ).
cnf(d28,plain,
( ~ sum(X0,'additive$uinverse'(b),'additive$uinverse'(b))
| sum(X1,d,d)
| ~ product('additive$uinverse'(a),X0,X1) ),
inference(resolution,[status(thm)],[d27,c1]) ).
cnf(d29,plain,
( ~ sum(X0,'additive$uinverse'(b),'additive$uinverse'(b))
| sum(multiply('additive$uinverse'(a),X0),d,d) ),
inference(resolution,[status(thm)],[d28,c5]) ).
cnf(d30,plain,
sum(multiply('additive$uinverse'(a),'additive$uidentity'),d,d),
inference(resolution,[status(thm)],[d29,c3]) ).
cnf(d31,plain,
d = add(multiply('additive$uinverse'(a),'additive$uidentity'),d),
inference(resolution,[status(thm)],[d30,d7]) ).
cnf(d32,plain,
d = add(d,multiply('additive$uinverse'(a),'additive$uidentity')),
inference(demodulation,[status(thm)],[d31,d6]) ).
cnf(d33,plain,
sum(d,'additive$uinverse'(d),multiply('additive$uinverse'(a),'additive$uidentity')),
inference(superposition,[status(thm)],[d32,d11]) ).
cnf(d34,plain,
multiply('additive$uinverse'(a),'additive$uidentity') = 'additive$uidentity',
inference(resolution,[status(thm)],[d33,d8]) ).
cnf(d35,plain,
( ~ sum(X1,X3,X5)
| sum(X2,X4,multiply(X0,X5))
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c5]) ).
cnf(d36,plain,
( ~ sum(X1,X3,X4)
| sum(X2,multiply(X0,X3),multiply(X0,X4))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d35,c5]) ).
cnf(d37,plain,
( ~ sum('additive$uinverse'(b),X0,X1)
| sum(d,multiply('additive$uinverse'(a),X0),multiply('additive$uinverse'(a),X1)) ),
inference(resolution,[status(thm)],[d36,c1]) ).
cnf(d38,plain,
sum(d,multiply('additive$uinverse'(a),b),multiply('additive$uinverse'(a),'additive$uidentity')),
inference(resolution,[status(thm)],[d37,c7]) ).
cnf(d39,plain,
sum(d,multiply('additive$uinverse'(a),b),'additive$uidentity'),
inference(demodulation,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
'additive$uidentity' = add(d,multiply('additive$uinverse'(a),b)),
inference(resolution,[status(thm)],[d39,d7]) ).
cnf(d41,plain,
sum('additive$uidentity','additive$uinverse'(multiply('additive$uinverse'(a),b)),d),
inference(superposition,[status(thm)],[d40,d26]) ).
cnf(d42,plain,
d = 'additive$uinverse'(multiply('additive$uinverse'(a),b)),
inference(resolution,[status(thm)],[d41,d0]) ).
cnf(d43,plain,
'additive$uinverse'(d) = multiply('additive$uinverse'(a),b),
inference(superposition,[status(thm)],[d42,d24]) ).
cnf(d44,plain,
( sum(multiply(X3,X1),X2,multiply(X4,X1))
| ~ sum(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d12,c5]) ).
cnf(d45,plain,
( sum(multiply(X0,b),c,multiply(X1,b))
| ~ sum(X0,a,X1) ),
inference(resolution,[status(thm)],[d44,c0]) ).
cnf(d46,plain,
sum(multiply('additive$uinverse'(a),b),c,multiply('additive$uidentity',b)),
inference(resolution,[status(thm)],[d45,c7]) ).
cnf(d47,plain,
sum('additive$uinverse'(d),c,multiply('additive$uidentity',b)),
inference(demodulation,[status(thm)],[d46,d43]) ).
cnf(d48,plain,
sum('additive$uinverse'(d),c,'additive$uidentity'),
inference(demodulation,[status(thm)],[d47,d19]) ).
cnf(d49,plain,
'additive$uidentity' = add('additive$uinverse'(d),c),
inference(resolution,[status(thm)],[d48,d7]) ).
cnf(d50,plain,
'additive$uidentity' = add(c,'additive$uinverse'(d)),
inference(demodulation,[status(thm)],[d49,d6]) ).
cnf(d51,plain,
sum('additive$uidentity',d,c),
inference(superposition,[status(thm)],[d50,d3]) ).
cnf(d52,plain,
c = d,
inference(resolution,[status(thm)],[d51,d0]) ).
cnf(d53,plain,
c != c,
inference(demodulation,[status(thm)],[c2,d52]) ).
cnf(d54,plain,
add(X0,'additive$uidentity') = X0,
inference(resolution,[status(thm)],[d20,c6]) ).
cnf(d55,plain,
( ~ sum(X0,X2,b)
| sum(X1,X3,c)
| ~ product(a,X2,X3)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[c14,c0]) ).
cnf(d56,plain,
( ~ sum(X0,b,b)
| sum(X1,c,c)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[d55,c0]) ).
cnf(d57,plain,
( ~ sum(X0,b,b)
| sum(multiply(a,X0),c,c) ),
inference(resolution,[status(thm)],[d56,c5]) ).
cnf(d58,plain,
sum(multiply(a,'additive$uidentity'),c,c),
inference(resolution,[status(thm)],[d57,c3]) ).
cnf(d59,plain,
c = add(multiply(a,'additive$uidentity'),c),
inference(resolution,[status(thm)],[d58,d7]) ).
cnf(d60,plain,
c = add(c,multiply(a,'additive$uidentity')),
inference(demodulation,[status(thm)],[d59,d6]) ).
cnf(d61,plain,
sum(c,'additive$uinverse'(c),multiply(a,'additive$uidentity')),
inference(superposition,[status(thm)],[d60,d11]) ).
cnf(d62,plain,
multiply(a,'additive$uidentity') = 'additive$uidentity',
inference(resolution,[status(thm)],[d61,d8]) ).
cnf(d63,plain,
c = add(c,'additive$uidentity'),
inference(demodulation,[status(thm)],[d60,d62]) ).
cnf(d64,plain,
c = c,
inference(demodulation,[status(thm)],[d63,d54]) ).
cnf(d65,plain,
$false,
inference(resolution,[status(thm)],[d64,d53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n004.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sat Sep 26 05:43:42 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.21/13.56 % SZS status Unsatisfiable for theBenchmark.p
% 9.21/13.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------