%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG006-2 : 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 : n007.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 4.13s 14.94s
% Output : CNFRefutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of clauses : 52 ( 28 unt; 0 nHn; 44 RR)
% Number of literals : 96 ( 0 equ; 46 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 96 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_substitution1,axiom,
( product(X1,X2,X3)
| ~ product(X0,X2,X3)
| ~ equalish(X0,X1) ) ).
cnf(product_substitution2,axiom,
( product(X2,X1,X3)
| ~ product(X2,X0,X3)
| ~ equalish(X0,X1) ) ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
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(distributivity2,axiom,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(addition_is_well_defined,axiom,
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(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(c6,plain,
( product(X3,X1,X2)
| ~ equalish(X0,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_substitution1]) ).
cnf(c7,plain,
( product(X0,X3,X2)
| ~ equalish(X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_substitution2]) ).
cnf(c9,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c10,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c14,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c15,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(c17,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c21,plain,
( ~ sum(X4,X6,X2)
| ~ sum(X3,X5,X1)
| ~ product(X0,X5,X6)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c24,plain,
( equalish(X3,X2)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c29,plain,
( product('additive$uinverse'(X0),X1,'additive$uinverse'(X2))
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_lemma2]) ).
cnf(c30,plain,
( product('additive$uinverse'(X0),'additive$uinverse'(X1),X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_lemma3]) ).
cnf(c31,plain,
sum(b,'additive$uinverse'(c),'bS$uIc'),
inference(clausification,[status(esa)],[b_plus_inverse_c]) ).
cnf(c32,plain,
product(a,b,aPb),
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c33,plain,
product(a,c,aPc),
inference(clausification,[status(esa)],[a_times_c]) ).
cnf(c34,plain,
sum(aPb,'additive$uinverse'(aPc),'aPb$uS$uIaPc'),
inference(clausification,[status(esa)],[aPb_plus_IaPc]) ).
cnf(c35,plain,
~ product(a,'bS$uIc','aPb$uS$uIaPc'),
inference(clausification,[status(esa)],[prove_a_times_bS_Ic_is_aPb_S__IaPc]) ).
cnf(d0,plain,
( ~ sum(X1,'additive$uidentity',X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c24,c10]) ).
cnf(d1,plain,
( ~ sum(X3,X0,'additive$uidentity')
| sum(X3,X2,X1)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c9]) ).
cnf(d2,plain,
( ~ sum('additive$uinverse'(X0),X2,X1)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d1,c14]) ).
cnf(d3,plain,
sum(X0,'additive$uidentity','additive$uinverse'('additive$uinverse'(X0))),
inference(resolution,[status(thm)],[d2,c14]) ).
cnf(d4,plain,
equalish('additive$uinverse'('additive$uinverse'(X0)),X0),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ product('additive$uinverse'('additive$uinverse'(X0)),X1,X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
product('additive$uinverse'(a),c,'additive$uinverse'(aPc)),
inference(resolution,[status(thm)],[c29,c33]) ).
cnf(d7,plain,
product('additive$uinverse'('additive$uinverse'(a)),'additive$uinverse'(c),'additive$uinverse'(aPc)),
inference(resolution,[status(thm)],[d6,c30]) ).
cnf(d8,plain,
sum('additive$uinverse'(c),b,'bS$uIc'),
inference(resolution,[status(thm)],[c17,c31]) ).
cnf(d9,plain,
sum('additive$uinverse'(aPc),aPb,'aPb$uS$uIaPc'),
inference(resolution,[status(thm)],[c17,c34]) ).
cnf(d10,plain,
( ~ product(X3,X0,'additive$uinverse'(aPc))
| ~ product(X3,X1,aPb)
| product(X3,X2,'aPb$uS$uIaPc')
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c21,d9]) ).
cnf(d11,plain,
( ~ product(X0,'additive$uinverse'(c),'additive$uinverse'(aPc))
| ~ product(X0,b,aPb)
| product(X0,'bS$uIc','aPb$uS$uIaPc') ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( product('additive$uinverse'('additive$uinverse'(a)),'bS$uIc','aPb$uS$uIaPc')
| ~ product('additive$uinverse'('additive$uinverse'(a)),b,aPb) ),
inference(resolution,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
product('additive$uinverse'(a),'additive$uinverse'(b),aPb),
inference(resolution,[status(thm)],[c30,c32]) ).
cnf(d14,plain,
product('additive$uinverse'('additive$uinverse'(a)),'additive$uinverse'('additive$uinverse'(b)),aPb),
inference(resolution,[status(thm)],[d13,c30]) ).
cnf(d15,plain,
( ~ product(X0,'additive$uinverse'('additive$uinverse'(X1)),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d16,plain,
product('additive$uinverse'('additive$uinverse'(a)),b,aPb),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
product('additive$uinverse'('additive$uinverse'(a)),'bS$uIc','aPb$uS$uIaPc'),
inference(resolution,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
product(a,'bS$uIc','aPb$uS$uIaPc'),
inference(resolution,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c35,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-2 : 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 : n007.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 05:41:53 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.13/14.94 % SZS status Unsatisfiable for theBenchmark.p
% 4.13/14.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------