%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC207+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 02:41:52 PM UTC 2026
% Result : Theorem 0.12s 5.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC207+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.35 % Computer : n004.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.35 % CPULimit : 300
% 0.08/5.35 % WCLimit : 300
% 0.08/5.35 % DateTime : Mon Sep 21 08:04:56 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.38 % Drodi V4.1.1
% 0.12/5.42 % Refutation found
% 0.12/5.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/5.42 % SZS output start CNFRefutation for theBenchmark
% 0.12/5.42 fof(f4,axiom,(
% 0.12/5.42 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.12/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/5.42 fof(f15,axiom,(
% 0.12/5.42 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.12/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/5.42 fof(f16,axiom,(
% 0.12/5.42 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.12/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/5.42 fof(f17,axiom,(
% 0.12/5.42 ssList(nil) ),
% 0.12/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/5.42 fof(f39,axiom,(
% 0.12/5.42 ~ singletonP(nil) ),
% 0.12/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/5.42 fof(f96,conjecture,(
% 0.12/5.42 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| neq(U,nil)| ( (! [Y] :( ssItem(Y)=> ( cons(Y,nil) != W| ~ memberP(X,Y)| (? [Z] :( ssItem(Z)& Y != Z& memberP(X,Z)& leq(Y,Z) ) )) ))& ( nil != X| nil != W ) ) ) ) )) )) )) )),
% 0.12/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/5.42 fof(f97,negated_conjecture,(
% 0.12/5.42 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| neq(U,nil)| ( (! [Y] :( ssItem(Y)=> ( cons(Y,nil) != W| ~ memberP(X,Y)| (? [Z] :( ssItem(Z)& Y != Z& memberP(X,Z)& leq(Y,Z) ) )) ))& ( nil != X| nil != W ) ) ) ) )) )) )) ))),
% 0.12/5.42 inference(negated_conjecture,[status(cth)],[f96])).
% 0.12/5.42 fof(f113,plain,(
% 0.12/5.42 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.12/5.42 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.12/5.42 fof(f114,plain,(
% 0.12/5.42 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.12/5.42 inference(NNF_transformation,[status(thm)],[f113])).
% 0.12/5.42 fof(f115,plain,(
% 0.12/5.42 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.12/5.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.12/5.42 fof(f118,plain,(
% 0.12/5.42 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.12/5.42 inference(cnf_transformation,[status(thm)],[f115])).
% 0.12/5.42 fof(f217,plain,(
% 0.12/5.42 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.12/5.42 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.12/5.42 fof(f218,plain,(
% 0.12/5.42 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.12/5.42 inference(NNF_transformation,[status(thm)],[f217])).
% 0.12/5.42 fof(f220,plain,(
% 0.12/5.42 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.12/5.42 inference(cnf_transformation,[status(thm)],[f218])).
% 0.12/5.42 fof(f221,plain,(
% 0.12/5.42 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.12/5.42 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.12/5.42 fof(f222,plain,(
% 0.12/5.42 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.12/5.42 inference(cnf_transformation,[status(thm)],[f221])).
% 0.12/5.42 fof(f223,plain,(
% 0.12/5.42 ssList(nil)),
% 0.12/5.42 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/5.43 fof(f280,plain,(
% 0.12/5.43 ~singletonP(nil)),
% 0.12/5.43 inference(cnf_transformation,[status(thm)],[f39])).
% 0.12/5.43 fof(f415,plain,(
% 0.12/5.43 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&neq(V,nil))&~neq(U,nil))&((?[Y]: (ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Y,Z))))))|(nil=X&nil=W)))))))))))),
% 0.12/5.43 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.12/5.43 fof(f416,definition,(
% 0.12/5.43 ![W,X,Y]: (sP0_prd(Y,X,W)<=>(ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Y,Z))))))),
% 0.12/5.43 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.12/5.43 fof(f417,plain,(
% 0.12/5.43 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&neq(V,nil))&~neq(U,nil))&((?[Y]: sP0_prd(Y,X,W))|(nil=X&nil=W))))))))))),
% 0.12/5.43 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.12/5.43 fof(f418,plain,(
% 0.12/5.43 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&neq(sK48_skl,nil))&~neq(sK47_skl,nil))&(sP0_prd(sK51_skl,sK50_skl,sK49_skl)|(nil=sK50_skl&nil=sK49_skl)))))))),
% 0.12/5.43 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(Y,sK51_skl)],[f417])).
% 0.12/5.43 fof(f419,plain,(
% 0.12/5.43 ssList(sK47_skl)),
% 0.12/5.43 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/5.43 fof(f423,plain,(
% 0.12/5.43 sK48_skl=sK50_skl),
% 0.12/5.43 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/5.43 fof(f424,plain,(
% 0.12/5.43 sK47_skl=sK49_skl),
% 0.12/5.43 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/5.43 fof(f425,plain,(
% 0.12/5.43 neq(sK48_skl,nil)),
% 0.12/5.43 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/5.43 fof(f426,plain,(
% 0.12/5.43 ~neq(sK47_skl,nil)),
% 0.12/5.43 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/5.43 fof(f427,plain,(
% 0.12/5.43 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|nil=sK50_skl),
% 0.12/5.43 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/5.43 fof(f429,plain,(
% 0.12/5.43 ![W,X,Y]: ((~sP0_prd(Y,X,W)|(ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Y,Z))))))&(sP0_prd(Y,X,W)|(~ssItem(Y)|((~cons(Y,nil)=W|~memberP(X,Y))|(?[Z]: (((ssItem(Z)&~Y=Z)&memberP(X,Z))&leq(Y,Z)))))))),
% 0.12/5.43 inference(NNF_transformation,[status(thm)],[f416])).
% 0.12/5.43 fof(f430,plain,(
% 0.12/5.43 (![W,X,Y]: (~sP0_prd(Y,X,W)|(ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Y,Z)))))))&(![W,X,Y]: (sP0_prd(Y,X,W)|(~ssItem(Y)|((~cons(Y,nil)=W|~memberP(X,Y))|(?[Z]: (((ssItem(Z)&~Y=Z)&memberP(X,Z))&leq(Y,Z)))))))),
% 0.12/5.43 inference(miniscoping,[status(thm)],[f429])).
% 0.12/5.43 fof(f431,plain,(
% 0.12/5.43 (![W,X,Y]: (~sP0_prd(Y,X,W)|(ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Y,Z)))))))&(![W,X,Y]: (sP0_prd(Y,X,W)|(~ssItem(Y)|((~cons(Y,nil)=W|~memberP(X,Y))|(((ssItem(sK52_skl(Y,X,W))&~Y=sK52_skl(Y,X,W))&memberP(X,sK52_skl(Y,X,W)))&leq(Y,sK52_skl(Y,X,W)))))))),
% 0.12/5.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl]),skolemize(Z,sK52_skl(Y,X,W))],[f430])).
% 0.12/5.43 fof(f432,plain,(
% 0.12/5.43 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssItem(X0))),
% 0.12/5.43 inference(cnf_transformation,[status(thm)],[f431])).
% 0.12/5.43 fof(f433,plain,(
% 0.12/5.43 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|cons(X0,nil)=X2)),
% 0.12/5.43 inference(cnf_transformation,[status(thm)],[f431])).
% 0.12/5.43 fof(f443,plain,(
% 0.12/5.43 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.12/5.43 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.12/5.43 fof(f481,plain,(
% 0.12/5.43 ~ssList(sK47_skl)|~ssList(nil)|sK47_skl=nil),
% 0.12/5.43 inference(resolution,[status(thm)],[f220,f426])).
% 0.12/5.43 fof(f483,plain,(
% 0.12/5.43 ~ssList(nil)|sK47_skl=nil),
% 0.12/5.43 inference(forward_subsumption_resolution,[status(thm)],[f481,f419])).
% 0.12/5.43 fof(f484,plain,(
% 0.12/5.43 ![X0]: (~ssList(nil)|~ssItem(X0)|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.12/5.43 inference(resolution,[status(thm)],[f222,f443])).
% 0.12/5.43 fof(f485,plain,(
% 0.12/5.43 ![X0]: (~ssList(nil)|~ssItem(X0)|singletonP(cons(X0,nil)))),
% 0.12/5.43 inference(duplicate_literals_removal,[status(thm)],[f484])).
% 0.12/5.43 fof(f486,plain,(
% 0.12/5.43 ![X0]: (~ssItem(X0)|singletonP(cons(X0,nil)))),
% 0.12/5.43 inference(forward_subsumption_resolution,[status(thm)],[f485,f223])).
% 0.12/5.43 fof(f491,plain,(
% 0.12/5.43 sP0_prd(sK51_skl,sK48_skl,sK49_skl)|nil=sK50_skl),
% 0.12/5.43 inference(forward_demodulation,[status(thm)],[f423,f427])).
% 0.12/5.43 fof(f492,plain,(
% 0.12/5.43 sP0_prd(sK51_skl,sK48_skl,sK47_skl)|nil=sK50_skl),
% 0.12/5.43 inference(forward_demodulation,[status(thm)],[f424,f491])).
% 0.12/5.43 fof(f493,plain,(
% 0.12/5.43 sP0_prd(sK51_skl,sK48_skl,sK47_skl)|nil=sK48_skl),
% 0.12/5.43 inference(forward_demodulation,[status(thm)],[f423,f492])).
% 0.12/5.43 fof(f494,plain,(
% 0.12/5.43 nil=sK48_skl|ssItem(sK51_skl)),
% 0.12/5.43 inference(resolution,[status(thm)],[f493,f432])).
% 0.12/5.43 fof(f523,plain,(
% 0.12/5.43 sP0_prd(sK51_skl,sK48_skl,sK47_skl)|sK47_skl=sK48_skl),
% 0.12/5.43 inference(backward_demodulation,[status(thm)],[f532,f493])).
% 0.12/5.43 fof(f526,plain,(
% 0.12/5.43 ~singletonP(sK47_skl)),
% 0.12/5.43 inference(backward_demodulation,[status(thm)],[f532,f280])).
% 0.12/5.43 fof(f527,plain,(
% 0.12/5.43 ~neq(sK47_skl,sK47_skl)),
% 0.12/5.43 inference(backward_demodulation,[status(thm)],[f532,f426])).
% 0.12/5.43 fof(f528,plain,(
% 0.12/5.43 neq(sK48_skl,sK47_skl)),
% 0.12/5.43 inference(backward_demodulation,[status(thm)],[f532,f425])).
% 0.12/5.43 fof(f532,plain,(
% 0.12/5.43 sK47_skl=nil),
% 0.12/5.43 inference(forward_subsumption_resolution,[status(thm)],[f483,f223])).
% 0.12/5.43 fof(f534,plain,(
% 0.12/5.43 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|cons(X0,sK47_skl)=X2)),
% 0.12/5.43 inference(forward_demodulation,[status(thm)],[f532,f433])).
% 0.12/5.43 fof(f576,plain,(
% 0.12/5.43 sK47_skl=sK48_skl|ssItem(sK51_skl)),
% 0.12/5.43 inference(forward_demodulation,[status(thm)],[f532,f494])).
% 0.12/5.43 fof(f609,plain,(
% 0.12/5.43 sK47_skl=sK48_skl|cons(sK51_skl,sK47_skl)=sK47_skl),
% 0.12/5.43 inference(resolution,[status(thm)],[f523,f534])).
% 0.12/5.43 fof(f656,plain,(
% 0.12/5.43 ![X0]: (~ssItem(X0)|singletonP(cons(X0,sK47_skl)))),
% 0.12/5.43 inference(forward_demodulation,[status(thm)],[f532,f486])).
% 0.12/5.43 fof(f949,plain,(
% 0.12/5.43 ~ssItem(sK51_skl)|singletonP(sK47_skl)|sK47_skl=sK48_skl),
% 0.12/5.43 inference(paramodulation,[status(thm)],[f609,f656])).
% 0.12/5.43 fof(f963,plain,(
% 0.12/5.43 singletonP(sK47_skl)|sK47_skl=sK48_skl),
% 0.12/5.43 inference(forward_subsumption_resolution,[status(thm)],[f949,f576])).
% 0.12/5.43 fof(f995,plain,(
% 0.12/5.43 neq(sK47_skl,sK47_skl)),
% 0.12/5.43 inference(backward_demodulation,[status(thm)],[f998,f528])).
% 0.12/5.43 fof(f998,plain,(
% 0.12/5.43 sK47_skl=sK48_skl),
% 0.12/5.43 inference(forward_subsumption_resolution,[status(thm)],[f963,f526])).
% 0.12/5.43 fof(f1002,plain,(
% 0.12/5.43 $false),
% 0.12/5.43 inference(forward_subsumption_resolution,[status(thm)],[f995,f527])).
% 0.12/5.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/5.46 % Elapsed time: 0.086489 seconds
% 0.12/5.46 % CPU time: 0.363603 seconds
% 0.12/5.46 % Total memory used: 114.478 MB
% 0.12/5.46 % Net memory used: 114.078 MB
%------------------------------------------------------------------------------