%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL092-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.10s 0.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL092-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 14:15:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.44 % Refutation found
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.44 fof(f2,axiom,(
% 0.10/0.44 (![P,Q]: (combK != comb_app(P,Q) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f8,axiom,(
% 0.10/0.44 (![P,Q]: (( ~ member(comb_app(P,Q),comb)| member(Q,comb) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f32,axiom,(
% 0.10/0.44 (![P]: (( ~ member(P,comb)| member(pair(P,P),parcontract) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f37,axiom,(
% 0.10/0.44 (![R]: (( ~ member(pair(combK,R),parcontract)| R = combK ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f40,axiom,(
% 0.10/0.44 (![P,Q,R]: (( ~ member(pair(comb_app(P,Q),R),parcontract)| ap_parcontractE_c1(P,Q,R)| ap_parcontractE_c2(P,Q,R)| ap_parcontractE_c3(P,Q,R)| ap_parcontractE_c4(P,Q,R) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f41,axiom,(
% 0.10/0.44 (![P,Q,R]: (( ~ ap_parcontractE_c1(P,Q,R)| member(comb_app(P,Q),comb) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f42,axiom,(
% 0.10/0.44 (![P,Q,R]: (( ~ ap_parcontractE_c1(P,Q,R)| R = comb_app(P,Q) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f45,axiom,(
% 0.10/0.44 (![P,Q,R]: (( ~ ap_parcontractE_c2(P,Q,R)| P = comb_app(combK,R) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f50,axiom,(
% 0.10/0.44 (![P,Q,R]: (( ~ ap_parcontractE_c3(P,Q,R)| P = comb_app(comb_app(combS,ap_parcontractE_sk1p(P,Q,R)),ap_parcontractE_sk1q(P,Q,R)) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f51,axiom,(
% 0.10/0.44 (![P,Q,R]: (( ~ ap_parcontractE_c4(P,Q,R)| member(pair(P,ap_parcontractE_sk2q(P,Q,R)),parcontract) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f52,axiom,(
% 0.10/0.44 (![P,Q,R]: (( ~ ap_parcontractE_c4(P,Q,R)| member(pair(Q,ap_parcontractE_sk2s(P,Q,R)),parcontract) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f53,axiom,(
% 0.10/0.44 (![P,Q,R]: (( ~ ap_parcontractE_c4(P,Q,R)| R = comb_app(ap_parcontractE_sk2q(P,Q,R),ap_parcontractE_sk2s(P,Q,R)) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f54,hypothesis,(
% 0.10/0.44 member(pair(comb_app(combK,p),r),parcontract) ),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f55,negated_conjecture,(
% 0.10/0.44 (![PP]: (( r != comb_app(combK,PP)| ~ member(pair(p,PP),parcontract) ) ))),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f57,plain,(
% 0.10/0.44 ![X0,X1]: (~combK=comb_app(X0,X1))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.44 fof(f66,plain,(
% 0.10/0.44 ![Q]: ((![P]: ~member(comb_app(P,Q),comb))|member(Q,comb))),
% 0.10/0.44 inference(miniscoping,[status(thm)],[f8])).
% 0.10/0.44 fof(f67,plain,(
% 0.10/0.44 ![X0,X1]: (~member(comb_app(X0,X1),comb)|member(X1,comb))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f66])).
% 0.10/0.44 fof(f97,plain,(
% 0.10/0.44 ![X0]: (~member(X0,comb)|member(pair(X0,X0),parcontract))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f32])).
% 0.10/0.44 fof(f103,plain,(
% 0.10/0.44 ![X0]: (~member(pair(combK,X0),parcontract)|X0=combK)),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f37])).
% 0.10/0.44 fof(f107,plain,(
% 0.10/0.44 ![X0,X1,X2]: (~member(pair(comb_app(X0,X1),X2),parcontract)|ap_parcontractE_c1(X0,X1,X2)|ap_parcontractE_c2(X0,X1,X2)|ap_parcontractE_c3(X0,X1,X2)|ap_parcontractE_c4(X0,X1,X2))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f40])).
% 0.10/0.44 fof(f108,plain,(
% 0.10/0.44 ![P,Q]: ((![R]: ~ap_parcontractE_c1(P,Q,R))|member(comb_app(P,Q),comb))),
% 0.10/0.44 inference(miniscoping,[status(thm)],[f41])).
% 0.10/0.44 fof(f109,plain,(
% 0.10/0.44 ![X0,X1,X2]: (~ap_parcontractE_c1(X0,X1,X2)|member(comb_app(X0,X1),comb))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f108])).
% 0.10/0.44 fof(f110,plain,(
% 0.10/0.44 ![X0,X1,X2]: (~ap_parcontractE_c1(X0,X1,X2)|X2=comb_app(X0,X1))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f42])).
% 0.10/0.44 fof(f115,plain,(
% 0.10/0.44 ![P,R]: ((![Q]: ~ap_parcontractE_c2(P,Q,R))|P=comb_app(combK,R))),
% 0.10/0.44 inference(miniscoping,[status(thm)],[f45])).
% 0.10/0.44 fof(f116,plain,(
% 0.10/0.44 ![X0,X1,X2]: (~ap_parcontractE_c2(X0,X1,X2)|X0=comb_app(combK,X2))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f115])).
% 0.10/0.44 fof(f122,plain,(
% 0.10/0.44 ![X0,X1,X2]: (~ap_parcontractE_c3(X0,X1,X2)|X0=comb_app(comb_app(combS,ap_parcontractE_sk1p(X0,X1,X2)),ap_parcontractE_sk1q(X0,X1,X2)))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f50])).
% 0.10/0.44 fof(f123,plain,(
% 0.10/0.44 ![X0,X1,X2]: (~ap_parcontractE_c4(X0,X1,X2)|member(pair(X0,ap_parcontractE_sk2q(X0,X1,X2)),parcontract))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f51])).
% 0.10/0.44 fof(f124,plain,(
% 0.10/0.44 ![X0,X1,X2]: (~ap_parcontractE_c4(X0,X1,X2)|member(pair(X1,ap_parcontractE_sk2s(X0,X1,X2)),parcontract))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f52])).
% 0.10/0.44 fof(f125,plain,(
% 0.10/0.44 ![X0,X1,X2]: (~ap_parcontractE_c4(X0,X1,X2)|X2=comb_app(ap_parcontractE_sk2q(X0,X1,X2),ap_parcontractE_sk2s(X0,X1,X2)))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f53])).
% 0.10/0.44 fof(f126,plain,(
% 0.10/0.44 member(pair(comb_app(combK,p),r),parcontract)),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f54])).
% 0.10/0.44 fof(f127,plain,(
% 0.10/0.44 ![X0]: (~r=comb_app(combK,X0)|~member(pair(p,X0),parcontract))),
% 0.10/0.44 inference(cnf_transformation,[status(thm)],[f55])).
% 0.10/0.44 fof(f311,plain,(
% 0.10/0.44 ap_parcontractE_c1(combK,p,r)|ap_parcontractE_c2(combK,p,r)|ap_parcontractE_c3(combK,p,r)|ap_parcontractE_c4(combK,p,r)),
% 0.10/0.44 inference(resolution,[status(thm)],[f107,f126])).
% 0.10/0.44 fof(f377,definition,(
% 0.10/0.44 sQ32_spl <=> (ap_parcontractE_c1(combK,p,r))),
% 0.10/0.44 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.10/0.44 fof(f378,plain,(
% 0.10/0.44 ap_parcontractE_c1(combK,p,r)|~sQ32_spl),
% 0.10/0.44 inference(component_clause,[status(thm)],[f377])).
% 0.10/0.44 fof(f380,definition,(
% 0.10/0.44 sQ33_spl <=> (ap_parcontractE_c2(combK,p,r))),
% 0.10/0.44 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.10/0.44 fof(f381,plain,(
% 0.10/0.44 ap_parcontractE_c2(combK,p,r)|~sQ33_spl),
% 0.10/0.44 inference(component_clause,[status(thm)],[f380])).
% 0.10/0.44 fof(f383,definition,(
% 0.10/0.44 sQ34_spl <=> (ap_parcontractE_c3(combK,p,r))),
% 0.10/0.44 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.10/0.44 fof(f384,plain,(
% 0.10/0.44 ap_parcontractE_c3(combK,p,r)|~sQ34_spl),
% 0.10/0.44 inference(component_clause,[status(thm)],[f383])).
% 0.10/0.44 fof(f386,definition,(
% 0.10/0.44 sQ35_spl <=> (ap_parcontractE_c4(combK,p,r))),
% 0.10/0.44 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.10/0.44 fof(f387,plain,(
% 0.10/0.44 ap_parcontractE_c4(combK,p,r)|~sQ35_spl),
% 0.10/0.44 inference(component_clause,[status(thm)],[f386])).
% 0.10/0.44 fof(f389,plain,(
% 0.10/0.44 sQ32_spl|sQ33_spl|sQ34_spl|sQ35_spl),
% 0.10/0.44 inference(split_clause,[status(thm)],[f311,f377,f380,f383,f386])).
% 0.10/0.44 fof(f414,plain,(
% 0.10/0.44 combK=comb_app(combK,r)|~sQ33_spl),
% 0.10/0.44 inference(resolution,[status(thm)],[f381,f116])).
% 0.10/0.44 fof(f417,plain,(
% 0.10/0.44 $false|~sQ33_spl),
% 0.10/0.44 inference(forward_subsumption_resolution,[status(thm)],[f414,f57])).
% 0.10/0.44 fof(f418,plain,(
% 0.10/0.44 ~sQ33_spl),
% 0.10/0.44 inference(contradiction_clause,[status(thm)],[f417])).
% 0.10/0.44 fof(f419,plain,(
% 0.10/0.44 member(comb_app(combK,p),comb)|~sQ32_spl),
% 0.10/0.44 inference(resolution,[status(thm)],[f378,f109])).
% 0.10/0.44 fof(f420,plain,(
% 0.10/0.44 r=comb_app(combK,p)|~sQ32_spl),
% 0.10/0.44 inference(resolution,[status(thm)],[f378,f110])).
% 0.10/0.44 fof(f475,plain,(
% 0.10/0.44 ~member(r,comb)|member(p,comb)|~sQ32_spl),
% 0.10/0.44 inference(paramodulation,[status(thm)],[f420,f67])).
% 0.10/0.44 fof(f483,definition,(
% 0.10/0.45 sQ36_spl <=> (member(r,comb))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f485,plain,(
% 0.10/0.45 ~member(r,comb)|sQ36_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f483])).
% 0.10/0.45 fof(f486,definition,(
% 0.10/0.45 sQ37_spl <=> (member(p,comb))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f487,plain,(
% 0.10/0.45 member(p,comb)|~sQ37_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f486])).
% 0.10/0.45 fof(f489,plain,(
% 0.10/0.45 ~sQ36_spl|sQ37_spl|~sQ32_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f475,f483,f486,f377])).
% 0.10/0.45 fof(f492,plain,(
% 0.10/0.45 combK=comb_app(comb_app(combS,ap_parcontractE_sk1p(combK,p,r)),ap_parcontractE_sk1q(combK,p,r))|~sQ34_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f122,f384])).
% 0.10/0.45 fof(f493,plain,(
% 0.10/0.45 $false|~sQ34_spl),
% 0.10/0.45 inference(forward_subsumption_resolution,[status(thm)],[f492,f57])).
% 0.10/0.45 fof(f494,plain,(
% 0.10/0.45 ~sQ34_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f493])).
% 0.10/0.45 fof(f514,plain,(
% 0.10/0.45 member(r,comb)|~sQ32_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f420,f419])).
% 0.10/0.45 fof(f515,plain,(
% 0.10/0.45 $false|sQ36_spl|~sQ32_spl),
% 0.10/0.45 inference(forward_subsumption_resolution,[status(thm)],[f514,f485])).
% 0.10/0.45 fof(f516,plain,(
% 0.10/0.45 sQ36_spl|~sQ32_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f515])).
% 0.10/0.45 fof(f519,plain,(
% 0.10/0.45 member(pair(combK,ap_parcontractE_sk2q(combK,p,r)),parcontract)|~sQ35_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f123,f387])).
% 0.10/0.45 fof(f520,plain,(
% 0.10/0.45 member(pair(p,ap_parcontractE_sk2s(combK,p,r)),parcontract)|~sQ35_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f124,f387])).
% 0.10/0.45 fof(f521,plain,(
% 0.10/0.45 r=comb_app(ap_parcontractE_sk2q(combK,p,r),ap_parcontractE_sk2s(combK,p,r))|~sQ35_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f125,f387])).
% 0.10/0.45 fof(f543,plain,(
% 0.10/0.45 member(pair(p,p),parcontract)|~sQ37_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f487,f97])).
% 0.10/0.45 fof(f706,plain,(
% 0.10/0.45 ~r=comb_app(combK,p)|~sQ37_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f543,f127])).
% 0.10/0.45 fof(f711,plain,(
% 0.10/0.45 ~r=r|~sQ32_spl|~sQ37_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f420,f706])).
% 0.10/0.45 fof(f712,plain,(
% 0.10/0.45 $false|~sQ32_spl|~sQ37_spl),
% 0.10/0.45 inference(trivial_equality_resolution,[status(thm)],[f711])).
% 0.10/0.45 fof(f713,plain,(
% 0.10/0.45 ~sQ32_spl|~sQ37_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f712])).
% 0.10/0.45 fof(f726,plain,(
% 0.10/0.45 ap_parcontractE_sk2q(combK,p,r)=combK|~sQ35_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f519,f103])).
% 0.10/0.45 fof(f732,plain,(
% 0.10/0.45 r=comb_app(combK,ap_parcontractE_sk2s(combK,p,r))|~sQ35_spl),
% 0.10/0.45 inference(backward_demodulation,[status(thm)],[f726,f521])).
% 0.10/0.45 fof(f737,plain,(
% 0.10/0.45 ~r=comb_app(combK,ap_parcontractE_sk2s(combK,p,r))|~sQ35_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f520,f127])).
% 0.10/0.45 fof(f742,plain,(
% 0.10/0.45 ~r=r|~sQ35_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f732,f737])).
% 0.10/0.45 fof(f743,plain,(
% 0.10/0.45 $false|~sQ35_spl),
% 0.10/0.45 inference(trivial_equality_resolution,[status(thm)],[f742])).
% 0.10/0.45 fof(f744,plain,(
% 0.10/0.45 ~sQ35_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f743])).
% 0.10/0.45 fof(f745,plain,(
% 0.10/0.45 $false),
% 0.10/0.45 inference(sat_refutation,[status(thm)],[f389,f418,f489,f494,f516,f713,f744])).
% 0.10/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.47 % Elapsed time: 0.087543 seconds
% 0.10/0.47 % CPU time: 0.484788 seconds
% 0.10/0.47 % Total memory used: 95.602 MB
% 0.10/0.47 % Net memory used: 95.060 MB
%------------------------------------------------------------------------------