%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC023+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 02:41:21 PM UTC 2026
% Result : Theorem 0.13s 10.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC023+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.36 % Computer : n016.cluster.edu
% 0.08/10.36 % Model : x86_64 x86_64
% 0.08/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.36 % Memory : 8046.5625MB
% 0.08/10.36 % OS : Linux 6.8.0-71-generic
% 0.08/10.36 % CPULimit : 300
% 0.08/10.36 % WCLimit : 300
% 0.08/10.36 % DateTime : Mon Sep 21 07:54:50 UTC 2026
% 0.08/10.36 % CPUTime :
% 0.08/10.38 % Drodi V4.1.1
% 0.13/10.40 % Refutation found
% 0.13/10.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/10.40 % SZS output start CNFRefutation for theBenchmark
% 0.13/10.40 fof(f17,axiom,(
% 0.13/10.40 ssList(nil) ),
% 0.13/10.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/10.40 fof(f42,axiom,(
% 0.13/10.40 (! [U] :( ssList(U)=> frontsegP(U,U) ) )),
% 0.13/10.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/10.40 fof(f45,axiom,(
% 0.13/10.40 (! [U] :( ssList(U)=> frontsegP(U,nil) ) )),
% 0.13/10.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/10.40 fof(f96,conjecture,(
% 0.13/10.40 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| (? [Y] :( ssList(Y)& neq(Y,nil)& frontsegP(V,Y)& frontsegP(U,Y) ))| ( (! [Z] :( ssList(Z)=> ( ~ neq(Z,nil)| ~ frontsegP(X,Z)| ~ frontsegP(W,Z) ) ))& ( nil != X| nil != W ) ) ) ) )) )) )) )),
% 0.13/10.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/10.40 fof(f97,negated_conjecture,(
% 0.13/10.40 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| (? [Y] :( ssList(Y)& neq(Y,nil)& frontsegP(V,Y)& frontsegP(U,Y) ))| ( (! [Z] :( ssList(Z)=> ( ~ neq(Z,nil)| ~ frontsegP(X,Z)| ~ frontsegP(W,Z) ) ))& ( nil != X| nil != W ) ) ) ) )) )) )) ))),
% 0.13/10.40 inference(negated_conjecture,[status(cth)],[f96])).
% 0.13/10.40 fof(f223,plain,(
% 0.13/10.40 ssList(nil)),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f17])).
% 0.13/10.40 fof(f285,plain,(
% 0.13/10.40 ![U]: (~ssList(U)|frontsegP(U,U))),
% 0.13/10.40 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 0.13/10.40 fof(f286,plain,(
% 0.13/10.40 ![X0]: (~ssList(X0)|frontsegP(X0,X0))),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f285])).
% 0.13/10.40 fof(f294,plain,(
% 0.13/10.40 ![U]: (~ssList(U)|frontsegP(U,nil))),
% 0.13/10.40 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 0.13/10.40 fof(f295,plain,(
% 0.13/10.40 ![X0]: (~ssList(X0)|frontsegP(X0,nil))),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f294])).
% 0.13/10.40 fof(f415,plain,(
% 0.13/10.40 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&neq(V,nil))&(![Y]: (((~ssList(Y)|~neq(Y,nil))|~frontsegP(V,Y))|~frontsegP(U,Y))))&((?[Z]: (ssList(Z)&((neq(Z,nil)&frontsegP(X,Z))&frontsegP(W,Z))))|(nil=X&nil=W)))))))))))),
% 0.13/10.40 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.13/10.40 fof(f416,definition,(
% 0.13/10.40 ![W,X,Z]: (sP0_prd(Z,X,W)<=>(ssList(Z)&((neq(Z,nil)&frontsegP(X,Z))&frontsegP(W,Z))))),
% 0.13/10.40 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.13/10.40 fof(f417,plain,(
% 0.13/10.40 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&neq(V,nil))&(![Y]: (((~ssList(Y)|~neq(Y,nil))|~frontsegP(V,Y))|~frontsegP(U,Y))))&((?[Z]: sP0_prd(Z,X,W))|(nil=X&nil=W))))))))))),
% 0.13/10.40 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.13/10.40 fof(f418,plain,(
% 0.13/10.40 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&neq(sK48_skl,nil))&(![Y]: (((~ssList(Y)|~neq(Y,nil))|~frontsegP(sK48_skl,Y))|~frontsegP(sK47_skl,Y))))&(sP0_prd(sK51_skl,sK50_skl,sK49_skl)|(nil=sK50_skl&nil=sK49_skl)))))))),
% 0.13/10.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Z,sK51_skl)],[f417])).
% 0.13/10.40 fof(f421,plain,(
% 0.13/10.40 ssList(sK49_skl)),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/10.40 fof(f422,plain,(
% 0.13/10.40 ssList(sK50_skl)),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/10.40 fof(f423,plain,(
% 0.13/10.40 sK48_skl=sK50_skl),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/10.40 fof(f424,plain,(
% 0.13/10.40 sK47_skl=sK49_skl),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/10.40 fof(f425,plain,(
% 0.13/10.40 neq(sK48_skl,nil)),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/10.40 fof(f426,plain,(
% 0.13/10.40 ![X0]: (~ssList(X0)|~neq(X0,nil)|~frontsegP(sK48_skl,X0)|~frontsegP(sK47_skl,X0))),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/10.40 fof(f427,plain,(
% 0.13/10.40 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|nil=sK50_skl),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/10.40 fof(f429,plain,(
% 0.13/10.40 ![W,X,Z]: ((~sP0_prd(Z,X,W)|(ssList(Z)&((neq(Z,nil)&frontsegP(X,Z))&frontsegP(W,Z))))&(sP0_prd(Z,X,W)|(~ssList(Z)|((~neq(Z,nil)|~frontsegP(X,Z))|~frontsegP(W,Z)))))),
% 0.13/10.40 inference(NNF_transformation,[status(thm)],[f416])).
% 0.13/10.40 fof(f430,plain,(
% 0.13/10.40 (![W,X,Z]: (~sP0_prd(Z,X,W)|(ssList(Z)&((neq(Z,nil)&frontsegP(X,Z))&frontsegP(W,Z)))))&(![W,X,Z]: (sP0_prd(Z,X,W)|(~ssList(Z)|((~neq(Z,nil)|~frontsegP(X,Z))|~frontsegP(W,Z)))))),
% 0.13/10.40 inference(miniscoping,[status(thm)],[f429])).
% 0.13/10.40 fof(f431,plain,(
% 0.13/10.40 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssList(X0))),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f430])).
% 0.13/10.40 fof(f432,plain,(
% 0.13/10.40 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|neq(X0,nil))),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f430])).
% 0.13/10.40 fof(f433,plain,(
% 0.13/10.40 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|frontsegP(X1,X0))),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f430])).
% 0.13/10.40 fof(f434,plain,(
% 0.13/10.40 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|frontsegP(X2,X0))),
% 0.13/10.40 inference(cnf_transformation,[status(thm)],[f430])).
% 0.13/10.40 fof(f436,definition,(
% 0.13/10.40 sQ0_spl <=> (sP0_prd(sK51_skl,sK50_skl,sK49_skl))),
% 0.13/10.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/10.40 fof(f437,plain,(
% 0.13/10.40 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|~sQ0_spl),
% 0.13/10.40 inference(component_clause,[status(thm)],[f436])).
% 0.13/10.41 fof(f439,definition,(
% 0.13/10.41 sQ1_spl <=> (nil=sK50_skl)),
% 0.13/10.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/10.41 fof(f440,plain,(
% 0.13/10.41 nil=sK50_skl|~sQ1_spl),
% 0.13/10.41 inference(component_clause,[status(thm)],[f439])).
% 0.13/10.41 fof(f442,plain,(
% 0.13/10.41 sQ0_spl|sQ1_spl),
% 0.13/10.41 inference(split_clause,[status(thm)],[f427,f436,f439])).
% 0.13/10.41 fof(f479,plain,(
% 0.13/10.41 neq(sK50_skl,nil)),
% 0.13/10.41 inference(forward_demodulation,[status(thm)],[f423,f425])).
% 0.13/10.41 fof(f481,plain,(
% 0.13/10.41 frontsegP(sK50_skl,sK50_skl)),
% 0.13/10.41 inference(resolution,[status(thm)],[f286,f422])).
% 0.13/10.41 fof(f485,plain,(
% 0.13/10.41 frontsegP(sK49_skl,nil)),
% 0.13/10.41 inference(resolution,[status(thm)],[f295,f421])).
% 0.13/10.41 fof(f490,plain,(
% 0.13/10.41 ssList(sK51_skl)|~sQ0_spl),
% 0.13/10.41 inference(resolution,[status(thm)],[f437,f431])).
% 0.13/10.41 fof(f493,plain,(
% 0.13/10.41 ![X0]: (~ssList(X0)|~neq(X0,nil)|~frontsegP(sK50_skl,X0)|~frontsegP(sK47_skl,X0))),
% 0.13/10.41 inference(forward_demodulation,[status(thm)],[f423,f426])).
% 0.13/10.41 fof(f494,plain,(
% 0.13/10.41 ![X0]: (~ssList(X0)|~neq(X0,nil)|~frontsegP(sK50_skl,X0)|~frontsegP(sK49_skl,X0))),
% 0.13/10.41 inference(forward_demodulation,[status(thm)],[f424,f493])).
% 0.13/10.41 fof(f495,plain,(
% 0.13/10.41 ~ssList(sK50_skl)|~frontsegP(sK50_skl,sK50_skl)|~frontsegP(sK49_skl,sK50_skl)),
% 0.13/10.41 inference(resolution,[status(thm)],[f494,f479])).
% 0.13/10.41 fof(f496,definition,(
% 0.13/10.41 sQ3_spl <=> (ssList(sK50_skl))),
% 0.13/10.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.13/10.41 fof(f498,plain,(
% 0.13/10.41 ~ssList(sK50_skl)|sQ3_spl),
% 0.13/10.41 inference(component_clause,[status(thm)],[f496])).
% 0.13/10.41 fof(f499,definition,(
% 0.13/10.41 sQ4_spl <=> (frontsegP(sK50_skl,sK50_skl))),
% 0.13/10.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.13/10.41 fof(f501,plain,(
% 0.13/10.41 ~frontsegP(sK50_skl,sK50_skl)|sQ4_spl),
% 0.13/10.41 inference(component_clause,[status(thm)],[f499])).
% 0.13/10.41 fof(f502,definition,(
% 0.13/10.41 sQ5_spl <=> (frontsegP(sK49_skl,sK50_skl))),
% 0.13/10.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.13/10.41 fof(f504,plain,(
% 0.13/10.41 ~frontsegP(sK49_skl,sK50_skl)|sQ5_spl),
% 0.13/10.41 inference(component_clause,[status(thm)],[f502])).
% 0.13/10.41 fof(f505,plain,(
% 0.13/10.41 ~sQ3_spl|~sQ4_spl|~sQ5_spl),
% 0.13/10.41 inference(split_clause,[status(thm)],[f495,f496,f499,f502])).
% 0.13/10.41 fof(f506,plain,(
% 0.13/10.41 frontsegP(sK50_skl,sK51_skl)|~sQ0_spl),
% 0.13/10.41 inference(resolution,[status(thm)],[f433,f437])).
% 0.13/10.41 fof(f507,plain,(
% 0.13/10.41 frontsegP(sK49_skl,sK51_skl)|~sQ0_spl),
% 0.13/10.41 inference(resolution,[status(thm)],[f434,f437])).
% 0.13/10.41 fof(f508,plain,(
% 0.13/10.41 neq(sK51_skl,nil)|~sQ0_spl),
% 0.13/10.41 inference(resolution,[status(thm)],[f432,f437])).
% 0.13/10.41 fof(f509,plain,(
% 0.13/10.41 ~ssList(sK51_skl)|~frontsegP(sK50_skl,sK51_skl)|~frontsegP(sK49_skl,sK51_skl)|~sQ0_spl),
% 0.13/10.41 inference(resolution,[status(thm)],[f508,f494])).
% 0.13/10.41 fof(f510,definition,(
% 0.13/10.41 sQ6_spl <=> (ssList(sK51_skl))),
% 0.13/10.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.13/10.41 fof(f512,plain,(
% 0.13/10.41 ~ssList(sK51_skl)|sQ6_spl),
% 0.13/10.41 inference(component_clause,[status(thm)],[f510])).
% 0.13/10.41 fof(f513,definition,(
% 0.13/10.41 sQ7_spl <=> (frontsegP(sK50_skl,sK51_skl))),
% 0.13/10.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.13/10.41 fof(f515,plain,(
% 0.13/10.41 ~frontsegP(sK50_skl,sK51_skl)|sQ7_spl),
% 0.13/10.41 inference(component_clause,[status(thm)],[f513])).
% 0.13/10.41 fof(f516,definition,(
% 0.13/10.41 sQ8_spl <=> (frontsegP(sK49_skl,sK51_skl))),
% 0.13/10.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.13/10.41 fof(f518,plain,(
% 0.13/10.41 ~frontsegP(sK49_skl,sK51_skl)|sQ8_spl),
% 0.13/10.41 inference(component_clause,[status(thm)],[f516])).
% 0.13/10.41 fof(f519,plain,(
% 0.13/10.41 ~sQ6_spl|~sQ7_spl|~sQ8_spl|~sQ0_spl),
% 0.13/10.41 inference(split_clause,[status(thm)],[f509,f510,f513,f516,f436])).
% 0.13/10.41 fof(f520,plain,(
% 0.13/10.41 $false|~sQ0_spl|sQ8_spl),
% 0.13/10.41 inference(forward_subsumption_resolution,[status(thm)],[f518,f507])).
% 0.13/10.41 fof(f521,plain,(
% 0.13/10.41 ~sQ0_spl|sQ8_spl),
% 0.13/10.41 inference(contradiction_clause,[status(thm)],[f520])).
% 0.13/10.41 fof(f524,plain,(
% 0.13/10.41 frontsegP(sK49_skl,sK50_skl)|~sQ1_spl),
% 0.13/10.41 inference(backward_demodulation,[status(thm)],[f440,f485])).
% 0.13/10.41 fof(f538,plain,(
% 0.13/10.41 $false|sQ5_spl|~sQ1_spl),
% 0.13/10.41 inference(forward_subsumption_resolution,[status(thm)],[f524,f504])).
% 0.13/10.41 fof(f539,plain,(
% 0.13/10.41 sQ5_spl|~sQ1_spl),
% 0.13/10.41 inference(contradiction_clause,[status(thm)],[f538])).
% 0.13/10.41 fof(f540,plain,(
% 0.13/10.41 $false|sQ3_spl),
% 0.13/10.41 inference(forward_subsumption_resolution,[status(thm)],[f498,f422])).
% 0.13/10.41 fof(f541,plain,(
% 0.13/10.41 sQ3_spl),
% 0.13/10.41 inference(contradiction_clause,[status(thm)],[f540])).
% 0.13/10.41 fof(f542,plain,(
% 0.13/10.41 $false|sQ6_spl|~sQ0_spl),
% 0.13/10.41 inference(forward_subsumption_resolution,[status(thm)],[f490,f512])).
% 0.13/10.41 fof(f543,plain,(
% 0.13/10.41 sQ6_spl|~sQ0_spl),
% 0.13/10.41 inference(contradiction_clause,[status(thm)],[f542])).
% 0.13/10.41 fof(f544,plain,(
% 0.13/10.41 $false|sQ4_spl),
% 0.13/10.41 inference(forward_subsumption_resolution,[status(thm)],[f501,f481])).
% 0.13/10.41 fof(f545,plain,(
% 0.13/10.41 sQ4_spl),
% 0.13/10.41 inference(contradiction_clause,[status(thm)],[f544])).
% 0.13/10.41 fof(f555,definition,(
% 0.13/10.41 sQ10_spl <=> (ssList(sK49_skl))),
% 0.13/10.41 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.13/10.41 fof(f557,plain,(
% 0.13/10.41 ~ssList(sK49_skl)|sQ10_spl),
% 0.13/10.41 inference(component_clause,[status(thm)],[f555])).
% 0.13/10.41 fof(f573,definition,(
% 0.13/10.41 sQ13_spl <=> (ssList(nil))),
% 0.13/10.41 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.13/10.41 fof(f575,plain,(
% 0.13/10.41 ~ssList(nil)|sQ13_spl),
% 0.13/10.41 inference(component_clause,[status(thm)],[f573])).
% 0.13/10.41 fof(f577,plain,(
% 0.13/10.41 $false|sQ10_spl),
% 0.13/10.41 inference(forward_subsumption_resolution,[status(thm)],[f557,f421])).
% 0.13/10.41 fof(f578,plain,(
% 0.13/10.41 sQ10_spl),
% 0.13/10.41 inference(contradiction_clause,[status(thm)],[f577])).
% 0.13/10.41 fof(f584,plain,(
% 0.13/10.41 $false|sQ13_spl),
% 0.13/10.41 inference(forward_subsumption_resolution,[status(thm)],[f575,f223])).
% 0.13/10.41 fof(f585,plain,(
% 0.13/10.41 sQ13_spl),
% 0.13/10.41 inference(contradiction_clause,[status(thm)],[f584])).
% 0.13/10.41 fof(f663,plain,(
% 0.13/10.41 $false|sQ7_spl|~sQ0_spl),
% 0.13/10.41 inference(forward_subsumption_resolution,[status(thm)],[f506,f515])).
% 0.13/10.41 fof(f664,plain,(
% 0.13/10.41 sQ7_spl|~sQ0_spl),
% 0.13/10.41 inference(contradiction_clause,[status(thm)],[f663])).
% 0.13/10.41 fof(f665,plain,(
% 0.13/10.41 $false),
% 0.13/10.41 inference(sat_refutation,[status(thm)],[f442,f505,f519,f521,f539,f541,f543,f545,f578,f585,f664])).
% 0.13/10.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/10.43 % Elapsed time: 0.068199 seconds
% 0.13/10.43 % CPU time: 0.184389 seconds
% 0.13/10.43 % Total memory used: 110.932 MB
% 0.13/10.43 % Net memory used: 110.757 MB
%------------------------------------------------------------------------------