%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG006-1 : 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 : n002.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 08:25:33 AM UTC 2026
% Result : Unsatisfiable 20.89s 7.56s
% Output : CNFRefutation 20.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of clauses : 71 ( 38 unt; 0 nHn; 54 RR)
% Number of literals : 129 ( 10 equ; 60 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 142 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_lemma1,axiom,
( product(X0,'additive$uinverse'(X1),'additive$uinverse'(X2))
| ~ product(X0,X1,X2) ) ).
cnf(product_lemma2,axiom,
( product('additive$uinverse'(X0),X1,'additive$uinverse'(X2))
| ~ product(X0,X1,X2) ) ).
cnf(product_lemma3,axiom,
( product('additive$uinverse'(X0),'additive$uinverse'(X1),X2)
| ~ product(X0,X1,X2) ) ).
cnf(b_plus_inverse_c,hypothesis,
sum(b,'additive$uinverse'(c),'bS$uIc') ).
cnf(a_times_b,hypothesis,
product(a,b,aPb) ).
cnf(a_times_c,hypothesis,
product(a,c,aPc) ).
cnf(aPb_plus_IaPc,hypothesis,
sum(aPb,'additive$uinverse'(aPc),'aPb$uS$uIaPc') ).
cnf(prove_a_times_bS_Ic_is_aPb_S__IaPc,negated_conjecture,
~ product(a,'bS$uIc','aPb$uS$uIaPc') ).
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(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,'additive$uinverse'(X1),'additive$uinverse'(X2))
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_lemma1]) ).
cnf(c1,plain,
( product('additive$uinverse'(X0),X1,'additive$uinverse'(X2))
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_lemma2]) ).
cnf(c2,plain,
( product('additive$uinverse'(X0),'additive$uinverse'(X1),X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_lemma3]) ).
cnf(c3,plain,
sum(b,'additive$uinverse'(c),'bS$uIc'),
inference(clausification,[status(esa)],[b_plus_inverse_c]) ).
cnf(c4,plain,
product(a,b,aPb),
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c5,plain,
product(a,c,aPc),
inference(clausification,[status(esa)],[a_times_c]) ).
cnf(c6,plain,
sum(aPb,'additive$uinverse'(aPc),'aPb$uS$uIaPc'),
inference(clausification,[status(esa)],[aPb_plus_IaPc]) ).
cnf(c7,plain,
~ product(a,'bS$uIc','aPb$uS$uIaPc'),
inference(clausification,[status(esa)],[prove_a_times_bS_Ic_is_aPb_S__IaPc]) ).
cnf(c8,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c9,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c10,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c11,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c12,plain,
sum('additive$uinverse'(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c13,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c14,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(c15,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(c16,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c19,plain,
( ~ product(X6,X5,X2)
| ~ product(X6,X4,X1)
| ~ product(X6,X3,X0)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c23,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c24,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ sum(X0,'additive$uidentity',X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c23,c9]) ).
cnf(d1,plain,
( ~ sum(X3,'additive$uinverse'(X2),X1)
| ~ sum(X0,X2,X3)
| sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[c14,c13]) ).
cnf(d2,plain,
( sum(X0,'additive$uidentity','aPb$uS$uIaPc')
| ~ sum(X0,aPc,aPb) ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
X0 = add(X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d0,c11]) ).
cnf(d4,plain,
( ~ sum(X4,X1,X3)
| ~ sum(X2,X4,X0)
| sum(X0,X1,add(X2,X3)) ),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(d5,plain,
( sum(X2,X1,add(X0,'additive$uidentity'))
| ~ sum(X0,'additive$uinverse'(X1),X2) ),
inference(resolution,[status(thm)],[d4,c12]) ).
cnf(d6,plain,
( ~ sum(X0,'additive$uinverse'(X2),X1)
| sum(X1,X2,X0) ),
inference(demodulation,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ sum(X2,'additive$uinverse'(c),X1)
| ~ sum(X0,b,X2)
| sum(X0,'bS$uIc',X1) ),
inference(resolution,[status(thm)],[c14,c3]) ).
cnf(d8,plain,
( sum(X0,'bS$uIc','additive$uinverse'(c))
| ~ sum(X0,b,'additive$uidentity') ),
inference(resolution,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
sum('additive$uinverse'(b),'bS$uIc','additive$uinverse'(c)),
inference(resolution,[status(thm)],[d8,c12]) ).
cnf(d10,plain,
product('additive$uinverse'(X0),X1,'additive$uinverse'(multiply(X0,X1))),
inference(resolution,[status(thm)],[c10,c1]) ).
cnf(d11,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c24,c10]) ).
cnf(d12,plain,
'additive$uinverse'(multiply(X0,X1)) = multiply('additive$uinverse'(X0),X1),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
product('additive$uinverse'(a),'additive$uinverse'(b),aPb),
inference(resolution,[status(thm)],[c2,c4]) ).
cnf(d14,plain,
( sum(X0,'additive$uidentity','additive$uinverse'(X1))
| ~ sum(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d15,plain,
sum(X0,'additive$uidentity','additive$uinverse'('additive$uinverse'(X0))),
inference(resolution,[status(thm)],[d14,c13]) ).
cnf(d16,plain,
X0 = 'additive$uinverse'('additive$uinverse'(X0)),
inference(resolution,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
product(a,'additive$uinverse'(c),'additive$uinverse'(aPc)),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d18,plain,
product('additive$uinverse'(a),'additive$uinverse'(c),'additive$uinverse'('additive$uinverse'(aPc))),
inference(resolution,[status(thm)],[d17,c1]) ).
cnf(d19,plain,
( ~ sum(X1,X5,X3)
| sum(X2,multiply(X0,X5),X4)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c19,c10]) ).
cnf(d20,plain,
( ~ sum(X0,X2,'additive$uinverse'(c))
| sum(X1,multiply('additive$uinverse'(a),X2),'additive$uinverse'('additive$uinverse'(aPc)))
| ~ product('additive$uinverse'(a),X0,X1) ),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
( ~ sum(X0,X2,'additive$uinverse'(c))
| sum(X1,multiply('additive$uinverse'(a),X2),aPc)
| ~ product('additive$uinverse'(a),X0,X1) ),
inference(demodulation,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
( ~ sum('additive$uinverse'(b),X0,'additive$uinverse'(c))
| sum(aPb,multiply('additive$uinverse'(a),X0),aPc) ),
inference(resolution,[status(thm)],[d21,d13]) ).
cnf(d23,plain,
( sum(aPb,'additive$uinverse'(multiply(a,X0)),aPc)
| ~ sum('additive$uinverse'(b),X0,'additive$uinverse'(c)) ),
inference(demodulation,[status(thm)],[d22,d12]) ).
cnf(d24,plain,
sum(aPb,'additive$uinverse'(multiply(a,'bS$uIc')),aPc),
inference(resolution,[status(thm)],[d23,d9]) ).
cnf(d25,plain,
sum(aPc,multiply(a,'bS$uIc'),aPb),
inference(resolution,[status(thm)],[d24,d6]) ).
cnf(d26,plain,
sum(multiply(a,'bS$uIc'),aPc,aPb),
inference(resolution,[status(thm)],[d25,c16]) ).
cnf(d27,plain,
sum(multiply(a,'bS$uIc'),'additive$uidentity','aPb$uS$uIaPc'),
inference(resolution,[status(thm)],[d26,d2]) ).
cnf(d28,plain,
multiply(a,'bS$uIc') = 'aPb$uS$uIaPc',
inference(resolution,[status(thm)],[d27,d0]) ).
cnf(d29,plain,
product(a,'bS$uIc','aPb$uS$uIaPc'),
inference(superposition,[status(thm)],[d28,c10]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[c7,d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 05:46:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.89/7.56 % SZS status Unsatisfiable for theBenchmark.p
% 20.89/7.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------