%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL089-1 : 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 : n012.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 7.86s 2.93s
% Output : CNFRefutation 7.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 14 unt; 0 nHn; 29 RR)
% Number of literals : 64 ( 0 equ; 39 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 35 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(comb_intros3,axiom,
( member('comb$uapp'(X0,X1),comb)
| ~ member(X1,comb)
| ~ member(X0,comb) ) ).
cnf(reduction_refl,axiom,
( member(pair(X0,X0),rtrancl(contract))
| ~ member(X0,comb) ) ).
cnf(reduction_rls_4,axiom,
( member(pair('comb$uapp'(X2,X0),X3),rtrancl(contract))
| ~ member(pair('comb$uapp'(X2,X1),X3),rtrancl(contract))
| ~ member(X2,comb)
| ~ member(pair(X0,X1),contract) ) ).
cnf(trans_rtrancl,axiom,
trans(rtrancl(X0)) ).
cnf(transD,axiom,
( member(pair(X1,X3),X0)
| ~ member(pair(X2,X3),X0)
| ~ member(pair(X1,X2),X0)
| ~ trans(X0) ) ).
cnf(contract_combD2,axiom,
( member(X1,comb)
| ~ member(pair(X0,X1),contract) ) ).
cnf(ap_reduce2_2h1,hypothesis,
member(r,comb) ).
cnf(ap_reduce2_2h4,hypothesis,
member(pair(y,z),contract) ).
cnf(ap_reduce2_2h5,hypothesis,
member(pair('comb$uapp'(r,p),'comb$uapp'(r,y)),rtrancl(contract)) ).
cnf(ap_reduce2_2c1,negated_conjecture,
~ member(pair('comb$uapp'(r,p),'comb$uapp'(r,z)),rtrancl(contract)) ).
cnf(c10,plain,
( member('comb$uapp'(X0,X1),comb)
| ~ member(X1,comb)
| ~ member(X0,comb) ),
inference(clausification,[status(esa)],[comb_intros3]) ).
cnf(c11,plain,
( member(pair(X0,X0),rtrancl(contract))
| ~ member(X0,comb) ),
inference(clausification,[status(esa)],[reduction_refl]) ).
cnf(c34,plain,
( member(pair('comb$uapp'(X2,X0),X3),rtrancl(contract))
| ~ member(pair('comb$uapp'(X2,X1),X3),rtrancl(contract))
| ~ member(X2,comb)
| ~ member(pair(X0,X1),contract) ),
inference(clausification,[status(esa)],[reduction_rls_4]) ).
cnf(c35,plain,
trans(rtrancl(X0)),
inference(clausification,[status(esa)],[trans_rtrancl]) ).
cnf(c36,plain,
( member(pair(X1,X3),X0)
| ~ member(pair(X2,X3),X0)
| ~ member(pair(X1,X2),X0)
| ~ trans(X0) ),
inference(clausification,[status(esa)],[transD]) ).
cnf(c37,plain,
( member(X1,comb)
| ~ member(pair(X0,X1),contract) ),
inference(clausification,[status(esa)],[contract_combD2]) ).
cnf(c38,plain,
member(r,comb),
inference(clausification,[status(esa)],[ap_reduce2_2h1]) ).
cnf(c41,plain,
member(pair(y,z),contract),
inference(clausification,[status(esa)],[ap_reduce2_2h4]) ).
cnf(c42,plain,
member(pair('comb$uapp'(r,p),'comb$uapp'(r,y)),rtrancl(contract)),
inference(clausification,[status(esa)],[ap_reduce2_2h5]) ).
cnf(c43,plain,
~ member(pair('comb$uapp'(r,p),'comb$uapp'(r,z)),rtrancl(contract)),
inference(clausification,[status(esa)],[ap_reduce2_2c1]) ).
cnf(d0,plain,
( ~ member('comb$uapp'(X0,X2),comb)
| member(pair('comb$uapp'(X0,X1),'comb$uapp'(X0,X2)),rtrancl(contract))
| ~ member(pair(X1,X2),contract)
| ~ member(X0,comb) ),
inference(resolution,[status(thm)],[c34,c11]) ).
cnf(d1,plain,
( ~ trans(rtrancl(contract))
| member(pair('comb$uapp'(r,p),X0),rtrancl(contract))
| ~ member(pair('comb$uapp'(r,y),X0),rtrancl(contract)) ),
inference(resolution,[status(thm)],[c36,c42]) ).
cnf(d2,plain,
( ~ member(pair('comb$uapp'(r,y),X0),rtrancl(contract))
| member(pair('comb$uapp'(r,p),X0),rtrancl(contract)) ),
inference(resolution,[status(thm)],[c35,d1]) ).
cnf(d3,plain,
( ~ member(pair(y,X0),contract)
| ~ member('comb$uapp'(r,X0),comb)
| ~ member(r,comb)
| member(pair('comb$uapp'(r,p),'comb$uapp'(r,X0)),rtrancl(contract)) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ member(pair(y,X0),contract)
| member(pair('comb$uapp'(r,p),'comb$uapp'(r,X0)),rtrancl(contract))
| ~ member('comb$uapp'(r,X0),comb) ),
inference(resolution,[status(thm)],[c38,d3]) ).
cnf(d5,plain,
( ~ member(pair(y,z),contract)
| ~ member('comb$uapp'(r,z),comb) ),
inference(resolution,[status(thm)],[d4,c43]) ).
cnf(d6,plain,
~ member('comb$uapp'(r,z),comb),
inference(resolution,[status(thm)],[c41,d5]) ).
cnf(d7,plain,
( ~ member(z,comb)
| ~ member(r,comb) ),
inference(resolution,[status(thm)],[d6,c10]) ).
cnf(d8,plain,
~ member(z,comb),
inference(resolution,[status(thm)],[c38,d7]) ).
cnf(d9,plain,
member(z,comb),
inference(resolution,[status(thm)],[c37,c41]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL089-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 23:12:34 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.86/2.93 % SZS status Unsatisfiable for theBenchmark.p
% 7.86/2.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------