%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL090-3 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 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 : Thu Sep 24 08:14:33 AM UTC 2026
% Result : Unsatisfiable 17.32s 17.60s
% Output : Proof 17.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of clauses : 60 ( 36 unt; 3 nHn; 60 RR)
% Number of literals : 95 ( 32 equ; 37 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 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 : 33 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_s,axiom,
combK != combS,
file('theBenchmark.p',k_s) ).
cnf(s_app,axiom,
combS != comb_app(P,Q),
file('theBenchmark.p',s_app) ).
cnf(app_app1,axiom,
( P1 = P2
| comb_app(P1,Q1) != comb_app(P2,Q2) ),
file('theBenchmark.p',app_app1) ).
cnf(app_app2,axiom,
( Q1 = Q2
| comb_app(P1,Q1) != comb_app(P2,Q2) ),
file('theBenchmark.p',app_app2) ).
cnf(app_app3,axiom,
( comb_app(P1,Q1) = comb_app(P2,Q2)
| Q1 != Q2
| P1 != P2 ),
file('theBenchmark.p',app_app3) ).
cnf(ap_contractE1,axiom,
( ap_contractE_c4(P,Q,R)
| ap_contractE_c3(P,Q,R)
| ap_contractE_c2(P,Q,R)
| ap_contractE_c1(P,Q,R)
| ~ member(pair(comb_app(P,Q),R),contract) ),
file('theBenchmark.p',ap_contractE1) ).
cnf(ap_contractE4,axiom,
( P = comb_app(combK,R)
| ~ ap_contractE_c1(P,Q,R) ),
file('theBenchmark.p',ap_contractE4) ).
cnf(ap_contractE9,axiom,
( P = comb_app(comb_app(combS,ap_contractE_sk1p(P,Q,R)),ap_contractE_sk1q(P,Q,R))
| ~ ap_contractE_c2(P,Q,R) ),
file('theBenchmark.p',ap_contractE9) ).
cnf(ap_contractE10,axiom,
( member(pair(P,ap_contractE_sk2q(P,Q,R)),contract)
| ~ ap_contractE_c3(P,Q,R) ),
file('theBenchmark.p',ap_contractE10) ).
cnf(ap_contractE13,axiom,
( member(pair(Q,ap_contractE_sk3q(P,Q,R)),contract)
| ~ ap_contractE_c4(P,Q,R) ),
file('theBenchmark.p',ap_contractE13) ).
cnf(k_contractE,axiom,
~ member(pair(combK,R),contract),
file('theBenchmark.p',k_contractE) ).
cnf(s_contractE,axiom,
~ member(pair(combS,R),contract),
file('theBenchmark.p',s_contractE) ).
cnf(i_contract_E,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
file('theBenchmark.p',i_contract_E) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
~ member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract),
inference(start,[status(thm),parent(0:0)],[k_contractE]) ).
cnf(t2,plain,
( ~ ap_contractE_c4(comb_app(combS,combK),combK,r)
| member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract) ),
inference(extension,[status(thm),parent(t1:1)],[ap_contractE13]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r)
| ~ member(pair(comb_app(comb_app(combS,combK),combK),r),contract)
| ap_contractE_c4(comb_app(combS,combK),combK,r) ),
inference(extension,[status(thm),parent(t2:2)],[ap_contractE1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
inference(extension,[status(thm),parent(t4:2)],[i_contract_E]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract)
| ~ ap_contractE_c3(comb_app(combS,combK),combK,r) ),
inference(extension,[status(thm),parent(t4:3)],[ap_contractE10]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract) ),
inference(extension,[status(thm),parent(t8:2)],[ap_contractE1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract)
| ~ ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(extension,[status(thm),parent(t10:2)],[ap_contractE13]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
~ member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract),
inference(extension,[status(thm),parent(t12:2)],[k_contractE]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( member(pair(combS,ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract)
| ~ ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(extension,[status(thm),parent(t10:3)],[ap_contractE10]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:3]) ).
cnf(t18,plain,
~ member(pair(combS,ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract),
inference(extension,[status(thm),parent(t16:2)],[s_contractE]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( combS = comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),ap_contractE_sk1q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)))
| ~ ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(extension,[status(thm),parent(t10:4)],[ap_contractE9]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t10:4]) ).
cnf(t22,plain,
combS != comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),ap_contractE_sk1q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),
inference(extension,[status(thm),parent(t20:2)],[s_app]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( combS = comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(extension,[status(thm),parent(t10:5)],[ap_contractE4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t10:5]) ).
cnf(t26,plain,
combS != comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)),
inference(extension,[status(thm),parent(t24:2)],[s_app]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( comb_app(combS,combK) = comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))
| ~ ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(extension,[status(thm),parent(t4:4)],[ap_contractE9]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t4:4]) ).
cnf(t30,plain,
( combS != comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))
| comb_app(comb_app(combS,combK),combS) = comb_app(comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r)),comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)))
| comb_app(combS,combK) != comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r)) ),
inference(extension,[status(thm),parent(t28:2)],[app_app3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( combS = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))
| comb_app(comb_app(combS,combK),combS) != comb_app(comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r)),comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))) ),
inference(extension,[status(thm),parent(t30:2)],[app_app2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
combS != comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),
inference(extension,[status(thm),parent(t32:2)],[s_app]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( comb_app(combS,combK) != comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))
| combS = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)) ),
inference(extension,[status(thm),parent(t30:3)],[app_app1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t30:3]) ).
cnf(t38,plain,
$false,
inference(reduction,[status(thm),parent(t36:2)],[t36:2,t28:2]) ).
cnf(t39,plain,
( comb_app(combS,combK) = comb_app(combK,r)
| ~ ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(extension,[status(thm),parent(t4:5)],[ap_contractE4]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t4:5]) ).
cnf(t41,plain,
( combS = combK
| comb_app(combS,combK) != comb_app(combK,r) ),
inference(extension,[status(thm),parent(t39:2)],[app_app1]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t39:2]) ).
cnf(t43,plain,
( combK = combS
| combS != combK ),
inference(extension,[status(thm),parent(t41:2)],[equality_2]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t41:2]) ).
cnf(t45,plain,
combK != combS,
inference(extension,[status(thm),parent(t43:2)],[k_s]) ).
cnf(t46,plain,
$false,
inference(connection,[status(thm),parent(t45:1)],[t45:1,t43:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL090-3 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.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 : Sun Sep 20 14:50:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 17.32/17.60 % SZS status Unsatisfiable for theBenchmark
% 17.32/17.60 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------