%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG006-3 : 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 : n011.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 5.69s 20.99s
% Output : CNFRefutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 51 ( 33 unt; 0 nHn; 37 RR)
% Number of literals : 86 ( 9 equ; 37 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 : 86 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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$uidentity',X0,X0) ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) ).
cnf(left_inverse,axiom,
sum('additive$uinverse'(X0),X0,'additive$uidentity') ).
cnf(right_inverse,axiom,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') ).
cnf(associativity_of_addition1,axiom,
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(commutativity_of_addition,axiom,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(c0,plain,
sum(b,'additive$uinverse'(c),'bS$uIc'),
inference(clausification,[status(esa)],[b_plus_inverse_c]) ).
cnf(c1,plain,
product(a,b,aPb),
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c2,plain,
product(a,c,aPc),
inference(clausification,[status(esa)],[a_times_c]) ).
cnf(c3,plain,
sum(aPb,'additive$uinverse'(aPc),'aPb$uS$uIaPc'),
inference(clausification,[status(esa)],[aPb_plus_IaPc]) ).
cnf(c4,plain,
~ product(a,'bS$uIc','aPb$uS$uIaPc'),
inference(clausification,[status(esa)],[prove_a_times_bS_Ic_is_aPb_S__IaPc]) ).
cnf(c5,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c7,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c8,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c9,plain,
sum('additive$uinverse'(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c10,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c11,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(c13,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c16,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(c20,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(d0,plain,
sum('additive$uinverse'(aPc),aPb,'aPb$uS$uIaPc'),
inference(resolution,[status(thm)],[c13,c3]) ).
cnf(d1,plain,
( ~ sum('additive$uinverse'(aPc),aPb,X0)
| X0 = 'aPb$uS$uIaPc' ),
inference(resolution,[status(thm)],[c20,d0]) ).
cnf(d2,plain,
( ~ sum(X0,X3,X1)
| ~ sum('additive$uidentity',X3,X2)
| sum('additive$uinverse'(X0),X1,X2) ),
inference(resolution,[status(thm)],[c11,c9]) ).
cnf(d3,plain,
( ~ sum('additive$uidentity',X1,X2)
| sum('additive$uinverse'(X0),add(X0,X1),X2) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
sum('additive$uinverse'(X0),add(X0,X1),X1),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c13,c8]) ).
cnf(d6,plain,
( ~ sum(X1,X2,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[c20,c8]) ).
cnf(d7,plain,
add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ sum(X2,X1,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[d5,c20]) ).
cnf(d9,plain,
sum('additive$uinverse'(c),b,'bS$uIc'),
inference(resolution,[status(thm)],[c13,c0]) ).
cnf(d10,plain,
( ~ sum('additive$uinverse'(X0),X3,X1)
| ~ sum('additive$uidentity',X3,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c10]) ).
cnf(d11,plain,
( ~ sum('additive$uidentity',b,X0)
| sum(c,'bS$uIc',X0) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
sum(c,'bS$uIc',b),
inference(resolution,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
( ~ product(X3,'bS$uIc',X1)
| ~ product(X3,c,X0)
| ~ product(X3,b,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d12,c16]) ).
cnf(d14,plain,
( ~ product(a,'bS$uIc',X1)
| ~ product(a,c,X0)
| sum(X0,X1,aPb) ),
inference(resolution,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
( ~ product(a,'bS$uIc',X0)
| sum(aPc,X0,aPb) ),
inference(resolution,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
sum(aPc,multiply(a,'bS$uIc'),aPb),
inference(resolution,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
aPb = add(multiply(a,'bS$uIc'),aPc),
inference(resolution,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
aPb = add(aPc,multiply(a,'bS$uIc')),
inference(demodulation,[status(thm)],[d17,d7]) ).
cnf(d19,plain,
sum('additive$uinverse'(aPc),aPb,multiply(a,'bS$uIc')),
inference(superposition,[status(thm)],[d18,d4]) ).
cnf(d20,plain,
multiply(a,'bS$uIc') = 'aPb$uS$uIaPc',
inference(resolution,[status(thm)],[d19,d1]) ).
cnf(d21,plain,
product(a,'bS$uIc','aPb$uS$uIaPc'),
inference(superposition,[status(thm)],[d20,c7]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[c4,d21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n011.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 05:44:28 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.69/20.99 % SZS status Unsatisfiable for theBenchmark.p
% 5.69/20.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------