%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL090-3 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(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 : Thu Sep 24 12:09:07 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL090-3 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:08:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.41 fof(f1,axiom,(
% 0.14/0.41 combK != combS ),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f3,axiom,(
% 0.14/0.41 (![P,Q]: (combS != comb_app(P,Q) ))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f4,axiom,(
% 0.14/0.41 (![P1,Q1,P2,Q2]: (( comb_app(P1,Q1) != comb_app(P2,Q2)| P1 = P2 ) ))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f7,axiom,(
% 0.14/0.41 (![P,Q,R]: (( ~ member(pair(comb_app(P,Q),R),contract)| ap_contractE_c1(P,Q,R)| ap_contractE_c2(P,Q,R)| ap_contractE_c3(P,Q,R)| ap_contractE_c4(P,Q,R) ) ))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f10,axiom,(
% 0.14/0.41 (![P,Q,R]: (( ~ ap_contractE_c1(P,Q,R)| P = comb_app(combK,R) ) ))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f15,axiom,(
% 0.14/0.41 (![P,Q,R]: (( ~ ap_contractE_c2(P,Q,R)| P = comb_app(comb_app(combS,ap_contractE_sk1p(P,Q,R)),ap_contractE_sk1q(P,Q,R)) ) ))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f16,axiom,(
% 0.14/0.41 (![P,Q,R]: (( ~ ap_contractE_c3(P,Q,R)| member(pair(P,ap_contractE_sk2q(P,Q,R)),contract) ) ))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f19,axiom,(
% 0.14/0.41 (![P,Q,R]: (( ~ ap_contractE_c4(P,Q,R)| member(pair(Q,ap_contractE_sk3q(P,Q,R)),contract) ) ))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f22,axiom,(
% 0.14/0.41 (![R]: (~ member(pair(combK,R),contract) ))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f23,axiom,(
% 0.14/0.41 (![R]: (~ member(pair(combS,R),contract) ))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f24,negated_conjecture,(
% 0.14/0.41 member(pair(comb_app(comb_app(combS,combK),combK),r),contract) ),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f25,plain,(
% 0.14/0.41 ~combK=combS),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.41 fof(f27,plain,(
% 0.14/0.41 ![X0,X1]: (~combS=comb_app(X0,X1))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.41 fof(f28,plain,(
% 0.14/0.41 ![P1,P2]: ((![Q1,Q2]: ~comb_app(P1,Q1)=comb_app(P2,Q2))|P1=P2)),
% 0.14/0.41 inference(miniscoping,[status(thm)],[f4])).
% 0.14/0.41 fof(f29,plain,(
% 0.14/0.41 ![X0,X1,X2,X3]: (~comb_app(X0,X1)=comb_app(X2,X3)|X0=X2)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f28])).
% 0.14/0.41 fof(f33,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~member(pair(comb_app(X0,X1),X2),contract)|ap_contractE_c1(X0,X1,X2)|ap_contractE_c2(X0,X1,X2)|ap_contractE_c3(X0,X1,X2)|ap_contractE_c4(X0,X1,X2))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f7])).
% 0.14/0.41 fof(f38,plain,(
% 0.14/0.41 ![P,R]: ((![Q]: ~ap_contractE_c1(P,Q,R))|P=comb_app(combK,R))),
% 0.14/0.41 inference(miniscoping,[status(thm)],[f10])).
% 0.14/0.41 fof(f39,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~ap_contractE_c1(X0,X1,X2)|X0=comb_app(combK,X2))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f38])).
% 0.14/0.41 fof(f45,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~ap_contractE_c2(X0,X1,X2)|X0=comb_app(comb_app(combS,ap_contractE_sk1p(X0,X1,X2)),ap_contractE_sk1q(X0,X1,X2)))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f15])).
% 0.14/0.41 fof(f46,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~ap_contractE_c3(X0,X1,X2)|member(pair(X0,ap_contractE_sk2q(X0,X1,X2)),contract))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f16])).
% 0.14/0.41 fof(f50,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~ap_contractE_c4(X0,X1,X2)|member(pair(X1,ap_contractE_sk3q(X0,X1,X2)),contract))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/0.41 fof(f54,plain,(
% 0.14/0.41 ![X0]: (~member(pair(combK,X0),contract))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f22])).
% 0.14/0.41 fof(f55,plain,(
% 0.14/0.41 ![X0]: (~member(pair(combS,X0),contract))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f23])).
% 0.14/0.41 fof(f56,plain,(
% 0.14/0.41 member(pair(comb_app(comb_app(combS,combK),combK),r),contract)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f24])).
% 0.14/0.41 fof(f59,plain,(
% 0.14/0.41 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)|ap_contractE_c4(comb_app(combS,combK),combK,r)),
% 0.14/0.41 inference(resolution,[status(thm)],[f33,f56])).
% 0.14/0.41 fof(f60,definition,(
% 0.14/0.41 sQ0_spl <=> (ap_contractE_c1(comb_app(combS,combK),combK,r))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f61,plain,(
% 0.14/0.41 ap_contractE_c1(comb_app(combS,combK),combK,r)|~sQ0_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f60])).
% 0.14/0.41 fof(f63,definition,(
% 0.14/0.41 sQ1_spl <=> (ap_contractE_c2(comb_app(combS,combK),combK,r))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f64,plain,(
% 0.14/0.41 ap_contractE_c2(comb_app(combS,combK),combK,r)|~sQ1_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f63])).
% 0.14/0.41 fof(f66,definition,(
% 0.14/0.41 sQ2_spl <=> (ap_contractE_c3(comb_app(combS,combK),combK,r))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f67,plain,(
% 0.14/0.41 ap_contractE_c3(comb_app(combS,combK),combK,r)|~sQ2_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f66])).
% 0.14/0.41 fof(f69,definition,(
% 0.14/0.41 sQ3_spl <=> (ap_contractE_c4(comb_app(combS,combK),combK,r))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f70,plain,(
% 0.14/0.41 ap_contractE_c4(comb_app(combS,combK),combK,r)|~sQ3_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f69])).
% 0.14/0.41 fof(f72,plain,(
% 0.14/0.41 sQ0_spl|sQ1_spl|sQ2_spl|sQ3_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f59,f60,f63,f66,f69])).
% 0.14/0.41 fof(f74,plain,(
% 0.14/0.41 member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract)|~sQ3_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f50,f70])).
% 0.14/0.41 fof(f75,plain,(
% 0.14/0.41 $false|~sQ3_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f74,f54])).
% 0.14/0.41 fof(f76,plain,(
% 0.14/0.41 ~sQ3_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f75])).
% 0.14/0.41 fof(f78,plain,(
% 0.14/0.41 member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract)|~sQ2_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f67,f46])).
% 0.14/0.41 fof(f87,plain,(
% 0.14/0.41 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))|~sQ2_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f78,f33])).
% 0.14/0.41 fof(f88,definition,(
% 0.14/0.41 sQ4_spl <=> (ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f89,plain,(
% 0.14/0.41 ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))|~sQ4_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f88])).
% 0.14/0.41 fof(f91,definition,(
% 0.14/0.41 sQ5_spl <=> (ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f92,plain,(
% 0.14/0.41 ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))|~sQ5_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f91])).
% 0.14/0.41 fof(f94,definition,(
% 0.14/0.41 sQ6_spl <=> (ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f95,plain,(
% 0.14/0.41 ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))|~sQ6_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f94])).
% 0.14/0.41 fof(f97,definition,(
% 0.14/0.41 sQ7_spl <=> (ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f98,plain,(
% 0.14/0.41 ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))|~sQ7_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f97])).
% 0.14/0.41 fof(f100,plain,(
% 0.14/0.41 sQ4_spl|sQ5_spl|sQ6_spl|sQ7_spl|~sQ2_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f87,f88,f91,f94,f97,f66])).
% 0.14/0.41 fof(f101,plain,(
% 0.14/0.41 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))|~sQ1_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f64,f45])).
% 0.14/0.41 fof(f106,plain,(
% 0.14/0.41 member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract)|~sQ7_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f98,f50])).
% 0.14/0.41 fof(f108,plain,(
% 0.14/0.41 $false|~sQ7_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f106,f54])).
% 0.14/0.41 fof(f109,plain,(
% 0.14/0.41 ~sQ7_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f108])).
% 0.14/0.41 fof(f111,plain,(
% 0.14/0.41 member(pair(combS,ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract)|~sQ6_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f95,f46])).
% 0.14/0.41 fof(f113,plain,(
% 0.14/0.41 $false|~sQ6_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f111,f55])).
% 0.14/0.41 fof(f114,plain,(
% 0.14/0.41 ~sQ6_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f113])).
% 0.14/0.41 fof(f115,plain,(
% 0.14/0.41 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)))|~sQ5_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f92,f45])).
% 0.14/0.41 fof(f120,plain,(
% 0.14/0.41 $false|~sQ5_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f115,f27])).
% 0.14/0.41 fof(f121,plain,(
% 0.14/0.41 ~sQ5_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f120])).
% 0.14/0.41 fof(f122,plain,(
% 0.14/0.41 combS=comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))|~sQ4_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f89,f39])).
% 0.14/0.41 fof(f125,plain,(
% 0.14/0.41 $false|~sQ4_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f122,f27])).
% 0.14/0.41 fof(f126,plain,(
% 0.14/0.41 ~sQ4_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f125])).
% 0.14/0.41 fof(f127,plain,(
% 0.14/0.41 comb_app(combS,combK)=comb_app(combK,r)|~sQ0_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f61,f39])).
% 0.14/0.41 fof(f167,plain,(
% 0.14/0.41 combS=comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))|~sQ1_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f101,f29])).
% 0.14/0.41 fof(f180,plain,(
% 0.14/0.41 $false|~sQ1_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f167,f27])).
% 0.14/0.41 fof(f181,plain,(
% 0.14/0.41 ~sQ1_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f180])).
% 0.14/0.41 fof(f198,plain,(
% 0.14/0.41 combS=combK|~sQ0_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f127,f29])).
% 0.14/0.41 fof(f219,plain,(
% 0.14/0.41 $false|~sQ0_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f198,f25])).
% 0.14/0.41 fof(f220,plain,(
% 0.14/0.41 ~sQ0_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f219])).
% 0.14/0.41 fof(f221,plain,(
% 0.14/0.41 $false),
% 0.14/0.41 inference(sat_refutation,[status(thm)],[f72,f76,f100,f109,f114,f121,f126,f181,f220])).
% 0.14/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.44 % Elapsed time: 0.059863 seconds
% 0.14/0.44 % CPU time: 0.170923 seconds
% 0.14/0.44 % Total memory used: 81.212 MB
% 0.14/0.44 % Net memory used: 80.887 MB
%------------------------------------------------------------------------------