%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL090-3 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 06:56:54 AM UTC 2026
% Result : Unsatisfiable 21.41s 3.19s
% Output : CNFRefutation 21.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 16 unt; 13 nHn; 42 RR)
% Number of literals : 87 ( 28 equ; 31 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 72 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_s,axiom,
combK != combS ).
cnf(s_app,axiom,
combS != 'comb$uapp'(X0,X1) ).
cnf(app_app1,axiom,
( X0 = X2
| 'comb$uapp'(X0,X1) != 'comb$uapp'(X2,X3) ) ).
cnf(ap_contractE1,axiom,
( 'ap$ucontractE$uc4'(X0,X1,X2)
| 'ap$ucontractE$uc3'(X0,X1,X2)
| 'ap$ucontractE$uc2'(X0,X1,X2)
| 'ap$ucontractE$uc1'(X0,X1,X2)
| ~ member(pair('comb$uapp'(X0,X1),X2),contract) ) ).
cnf(ap_contractE4,axiom,
( X0 = 'comb$uapp'(combK,X2)
| ~ 'ap$ucontractE$uc1'(X0,X1,X2) ) ).
cnf(ap_contractE9,axiom,
( X0 = 'comb$uapp'('comb$uapp'(combS,'ap$ucontractE$usk1p'(X0,X1,X2)),'ap$ucontractE$usk1q'(X0,X1,X2))
| ~ 'ap$ucontractE$uc2'(X0,X1,X2) ) ).
cnf(ap_contractE10,axiom,
( member(pair(X0,'ap$ucontractE$usk2q'(X0,X1,X2)),contract)
| ~ 'ap$ucontractE$uc3'(X0,X1,X2) ) ).
cnf(ap_contractE13,axiom,
( member(pair(X1,'ap$ucontractE$usk3q'(X0,X1,X2)),contract)
| ~ 'ap$ucontractE$uc4'(X0,X1,X2) ) ).
cnf(k_contractE,axiom,
~ member(pair(combK,X0),contract) ).
cnf(s_contractE,axiom,
~ member(pair(combS,X0),contract) ).
cnf(i_contract_E,negated_conjecture,
member(pair('comb$uapp'('comb$uapp'(combS,combK),combK),r),contract) ).
cnf(c0,plain,
combK != combS,
inference(clausification,[status(esa)],[k_s]) ).
cnf(c2,plain,
combS != 'comb$uapp'(X0,X1),
inference(clausification,[status(esa)],[s_app]) ).
cnf(c3,plain,
( X0 = X2
| 'comb$uapp'(X0,X1) != 'comb$uapp'(X2,X3) ),
inference(clausification,[status(esa)],[app_app1]) ).
cnf(c6,plain,
( 'ap$ucontractE$uc1'(X0,X1,X2)
| 'ap$ucontractE$uc3'(X0,X1,X2)
| ~ member(pair('comb$uapp'(X0,X1),X2),contract)
| 'ap$ucontractE$uc2'(X0,X1,X2)
| 'ap$ucontractE$uc4'(X0,X1,X2) ),
inference(clausification,[status(esa)],[ap_contractE1]) ).
cnf(c9,plain,
( X0 = 'comb$uapp'(combK,X2)
| ~ 'ap$ucontractE$uc1'(X0,X1,X2) ),
inference(clausification,[status(esa)],[ap_contractE4]) ).
cnf(c14,plain,
( X0 = 'comb$uapp'('comb$uapp'(combS,'ap$ucontractE$usk1p'(X0,X1,X2)),'ap$ucontractE$usk1q'(X0,X1,X2))
| ~ 'ap$ucontractE$uc2'(X0,X1,X2) ),
inference(clausification,[status(esa)],[ap_contractE9]) ).
cnf(c15,plain,
( member(pair(X0,'ap$ucontractE$usk2q'(X0,X1,X2)),contract)
| ~ 'ap$ucontractE$uc3'(X0,X1,X2) ),
inference(clausification,[status(esa)],[ap_contractE10]) ).
cnf(c18,plain,
( member(pair(X1,'ap$ucontractE$usk3q'(X0,X1,X2)),contract)
| ~ 'ap$ucontractE$uc4'(X0,X1,X2) ),
inference(clausification,[status(esa)],[ap_contractE13]) ).
cnf(c21,plain,
~ member(pair(combK,X0),contract),
inference(clausification,[status(esa)],[k_contractE]) ).
cnf(c22,plain,
~ member(pair(combS,X0),contract),
inference(clausification,[status(esa)],[s_contractE]) ).
cnf(c23,plain,
member(pair('comb$uapp'('comb$uapp'(combS,combK),combK),r),contract),
inference(clausification,[status(esa)],[i_contract_E]) ).
cnf(d0,plain,
( 'ap$ucontractE$uc4'('comb$uapp'(combS,combK),combK,r)
| 'ap$ucontractE$uc1'('comb$uapp'(combS,combK),combK,r)
| 'ap$ucontractE$uc3'('comb$uapp'(combS,combK),combK,r)
| 'ap$ucontractE$uc2'('comb$uapp'(combS,combK),combK,r) ),
inference(resolution,[status(thm)],[c23,c6]) ).
cnf(d1,plain,
~ 'ap$ucontractE$uc4'(X0,combK,X1),
inference(resolution,[status(thm)],[c18,c21]) ).
cnf(d2,plain,
( 'ap$ucontractE$uc1'('comb$uapp'(combS,combK),combK,r)
| 'ap$ucontractE$uc3'('comb$uapp'(combS,combK),combK,r)
| 'ap$ucontractE$uc2'('comb$uapp'(combS,combK),combK,r) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( 'comb$uapp'(combS,combK) = 'comb$uapp'(combK,r)
| 'ap$ucontractE$uc3'('comb$uapp'(combS,combK),combK,r)
| 'ap$ucontractE$uc2'('comb$uapp'(combS,combK),combK,r) ),
inference(resolution,[status(thm)],[d2,c9]) ).
cnf(d4,plain,
~ 'ap$ucontractE$uc3'(combS,X0,X1),
inference(resolution,[status(thm)],[c15,c22]) ).
cnf(d5,plain,
( 'ap$ucontractE$uc4'(X0,X1,'ap$ucontractE$usk2q'('comb$uapp'(X0,X1),X2,X3))
| 'ap$ucontractE$uc1'(X0,X1,'ap$ucontractE$usk2q'('comb$uapp'(X0,X1),X2,X3))
| 'ap$ucontractE$uc3'(X0,X1,'ap$ucontractE$usk2q'('comb$uapp'(X0,X1),X2,X3))
| 'ap$ucontractE$uc2'(X0,X1,'ap$ucontractE$usk2q'('comb$uapp'(X0,X1),X2,X3))
| ~ 'ap$ucontractE$uc3'('comb$uapp'(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[c15,c6]) ).
cnf(d6,plain,
( 'ap$ucontractE$uc1'(X0,combK,'ap$ucontractE$usk2q'('comb$uapp'(X0,combK),X1,X2))
| ~ 'ap$ucontractE$uc3'('comb$uapp'(X0,combK),X1,X2)
| 'ap$ucontractE$uc3'(X0,combK,'ap$ucontractE$usk2q'('comb$uapp'(X0,combK),X1,X2))
| 'ap$ucontractE$uc2'(X0,combK,'ap$ucontractE$usk2q'('comb$uapp'(X0,combK),X1,X2)) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( X0 = 'comb$uapp'(combK,'ap$ucontractE$usk2q'('comb$uapp'(X0,combK),X1,X2))
| ~ 'ap$ucontractE$uc3'('comb$uapp'(X0,combK),X1,X2)
| 'ap$ucontractE$uc3'(X0,combK,'ap$ucontractE$usk2q'('comb$uapp'(X0,combK),X1,X2))
| 'ap$ucontractE$uc2'(X0,combK,'ap$ucontractE$usk2q'('comb$uapp'(X0,combK),X1,X2)) ),
inference(resolution,[status(thm)],[d6,c9]) ).
cnf(d8,plain,
( ~ 'ap$ucontractE$uc3'('comb$uapp'(combS,combK),X0,X1)
| 'ap$ucontractE$uc2'(combS,combK,'ap$ucontractE$usk2q'('comb$uapp'(combS,combK),X0,X1))
| combS = 'comb$uapp'(combK,'ap$ucontractE$usk2q'('comb$uapp'(combS,combK),X0,X1)) ),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
( ~ 'ap$ucontractE$uc3'('comb$uapp'(combS,combK),X0,X1)
| 'ap$ucontractE$uc2'(combS,combK,'ap$ucontractE$usk2q'('comb$uapp'(combS,combK),X0,X1)) ),
inference(resolution,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
( combS = 'comb$uapp'('comb$uapp'(combS,'ap$ucontractE$usk1p'(combS,combK,'ap$ucontractE$usk2q'('comb$uapp'(combS,combK),X0,X1))),'ap$ucontractE$usk1q'(combS,combK,'ap$ucontractE$usk2q'('comb$uapp'(combS,combK),X0,X1)))
| ~ 'ap$ucontractE$uc3'('comb$uapp'(combS,combK),X0,X1) ),
inference(resolution,[status(thm)],[d9,c14]) ).
cnf(d11,plain,
~ 'ap$ucontractE$uc3'('comb$uapp'(combS,combK),X0,X1),
inference(resolution,[status(thm)],[c2,d10]) ).
cnf(d12,plain,
( 'ap$ucontractE$uc2'('comb$uapp'(combS,combK),combK,r)
| 'comb$uapp'(combS,combK) = 'comb$uapp'(combK,r) ),
inference(resolution,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
( 'comb$uapp'(combS,combK) = 'comb$uapp'('comb$uapp'(combS,'ap$ucontractE$usk1p'('comb$uapp'(combS,combK),combK,r)),'ap$ucontractE$usk1q'('comb$uapp'(combS,combK),combK,r))
| 'comb$uapp'(combS,combK) = 'comb$uapp'(combK,r) ),
inference(resolution,[status(thm)],[d12,c14]) ).
cnf(d14,plain,
( 'comb$uapp'(combS,combK) = 'comb$uapp'(combK,r)
| X0 = 'comb$uapp'(combS,'ap$ucontractE$usk1p'('comb$uapp'(combS,combK),combK,r))
| 'comb$uapp'(X0,X1) != 'comb$uapp'(combS,combK) ),
inference(superposition,[status(thm)],[d13,c3]) ).
cnf(d15,plain,
( 'comb$uapp'(combS,combK) = 'comb$uapp'(combK,r)
| combS = 'comb$uapp'(combS,'ap$ucontractE$usk1p'('comb$uapp'(combS,combK),combK,r)) ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
'comb$uapp'(combS,combK) = 'comb$uapp'(combK,r),
inference(resolution,[status(thm)],[c2,d15]) ).
cnf(d17,plain,
( X0 = combS
| 'comb$uapp'(X0,X1) != 'comb$uapp'(combK,r) ),
inference(superposition,[status(thm)],[d16,c3]) ).
cnf(d18,plain,
combK = combS,
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c0,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL090-3 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n006.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 23:13:10 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.41/3.19 % SZS status Unsatisfiable for theBenchmark.p
% 21.41/3.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------