%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC104-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 : Fri Sep 25 03:05:22 PM UTC 2026
% Result : Unsatisfiable 106.30s 15.63s
% Output : Proof 106.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 34
% Syntax : Number of formulae : 214 ( 146 unt; 0 def)
% Number of atoms : 422 ( 182 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 474 ( 266 ~; 208 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-4 aty)
% Number of variables : 186 ( 2 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t74,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t337,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t74]) ).
cnf(f114,axiom,
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
fof(f114_nnf,plain,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f114]) ).
fof(f114_sk,plain,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f114_nnf]) ).
cnf(c114,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(t137,plain,
or(not(eq(X1,X2)),or(not(neq(X1,X2)),or(not(ssList(X2)),not(ssList(X1))))) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(t609,plain,
or(not(eq(X1,X2)),or(not(neq(X1,X2)),or(not(ssList(X2)),not(ssList(X1))))) = true,
inference(orient,[status(thm)],[t137]) ).
cnf(f191,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f191_nnf,plain,
neq(sk2,nil),
inference(nnf_transformation,[status(thm)],[f191]) ).
cnf(c191,plain,
neq(sk2,nil),
inference(cnf_transformation,[status(esa)],[f191_nnf]) ).
cnf(t24,plain,
neq(sk2,nil) = true,
inference(equality_encoding,[status(esa)],[c191]) ).
cnf(t659,plain,
neq(sk2,nil) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(f189,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f189_nnf,plain,
sk2 = sk4,
inference(nnf_transformation,[status(thm)],[f189]) ).
cnf(c189,plain,
sk2 = sk4,
inference(cnf_transformation,[status(esa)],[f189_nnf]) ).
cnf(t1,plain,
sk4 = sk2,
inference(equality_encoding,[status(esa)],[c189]) ).
cnf(t680,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t1]) ).
cnf(t142314,plain,
neq(sk4,nil) = true,
inference(step,[status(thm)],[t659,t680]) ).
cnf(t681,plain,
neq(sk4,nil) = true,
inference(rw,[status(thm)],[t142314]) ).
cnf(t8616,plain,
neq(sk4,nil) = true,
inference(orient,[status(thm)],[t681]) ).
cnf(t8618,plain,
true = or(not(eq(sk4,nil)),or(not(true),or(not(ssList(nil)),not(ssList(sk4))))),
inference(cp,[status(thm)],[t609,t8616]) ).
cnf(t6,plain,
not(true) = false,
introduced(definition) ).
cnf(t622,plain,
not(true) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t142436,plain,
true = or(not(eq(sk4,nil)),or(false,or(not(ssList(nil)),not(ssList(sk4))))),
inference(step,[status(thm)],[t8618,t622]) ).
cnf(t27,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t266,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t27]) ).
cnf(t142437,plain,
true = or(not(eq(sk4,nil)),or(not(ssList(nil)),not(ssList(sk4)))),
inference(step,[status(thm)],[t142436,t266]) ).
cnf(f7,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f7_nnf,plain,
ssList(nil),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(t10,plain,
ssList(nil) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t686,plain,
ssList(nil) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t142438,plain,
true = or(not(eq(sk4,nil)),or(not(true),not(ssList(sk4)))),
inference(step,[status(thm)],[t142437,t686]) ).
cnf(t142439,plain,
true = or(not(eq(sk4,nil)),or(false,not(ssList(sk4)))),
inference(step,[status(thm)],[t142438,t622]) ).
cnf(t142440,plain,
true = or(not(eq(sk4,nil)),not(ssList(sk4))),
inference(step,[status(thm)],[t142439,t266]) ).
cnf(f188,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f188_nnf,plain,
ssList(sk4),
inference(nnf_transformation,[status(thm)],[f188]) ).
cnf(c188,plain,
ssList(sk4),
inference(cnf_transformation,[status(esa)],[f188_nnf]) ).
cnf(t14,plain,
ssList(sk4) = true,
inference(equality_encoding,[status(esa)],[c188]) ).
cnf(t1050,plain,
ssList(sk4) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t142441,plain,
true = or(not(eq(sk4,nil)),not(true)),
inference(step,[status(thm)],[t142440,t1050]) ).
cnf(t142442,plain,
true = or(not(eq(sk4,nil)),false),
inference(step,[status(thm)],[t142441,t622]) ).
cnf(t25,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t265,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t25]) ).
cnf(t142443,plain,
true = not(eq(sk4,nil)),
inference(step,[status(thm)],[t142442,t265]) ).
cnf(t9936,plain,
not(eq(sk4,nil)) = true,
inference(orient,[status(thm)],[t142443]) ).
cnf(t9937,plain,
false = ifeq(true,true,eq(sk4,nil),false),
inference(cp,[status(thm)],[t337,t9936]) ).
cnf(t71,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t223,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t71]) ).
cnf(t142444,plain,
false = eq(sk4,nil),
inference(step,[status(thm)],[t9937,t223]) ).
cnf(t9938,plain,
eq(sk4,nil) = false,
inference(orient,[status(thm)],[t142444]) ).
cnf(t76,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t236,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t76]) ).
cnf(f99,axiom,
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
fof(f99_nnf,plain,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f99]) ).
fof(f99_sk,plain,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f99_nnf]) ).
cnf(c99,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f99_sk]) ).
cnf(t134,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X2,X1),eq(X2,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
cnf(t424,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X2,X1),eq(X2,X1)),true),true) = true,
inference(orient,[status(thm)],[t134]) ).
cnf(f197,negated_conjecture,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f197_nnf,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(nnf_transformation,[status(thm)],[f197]) ).
fof(f197_sk,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(skolemisation,[status(esa)],[f197_nnf]) ).
cnf(c197,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(cnf_transformation,[status(esa)],[f197_sk]) ).
cnf(t96,plain,
or(not(neq(sk1,nil)),not(frontsegP(sk2,sk1))) = true,
inference(equality_encoding,[status(esa)],[c197]) ).
cnf(t617,plain,
or(not(neq(sk1,nil)),not(frontsegP(sk2,sk1))) = true,
inference(orient,[status(thm)],[t96]) ).
cnf(f190,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f190_nnf,plain,
sk1 = sk3,
inference(nnf_transformation,[status(thm)],[f190]) ).
cnf(c190,plain,
sk1 = sk3,
inference(cnf_transformation,[status(esa)],[f190_nnf]) ).
cnf(t0,plain,
sk3 = sk1,
inference(equality_encoding,[status(esa)],[c190]) ).
cnf(t666,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t0]) ).
cnf(t142310,plain,
or(not(neq(sk3,nil)),not(frontsegP(sk2,sk1))) = true,
inference(step,[status(thm)],[t617,t666]) ).
cnf(t142311,plain,
or(not(neq(sk3,nil)),not(frontsegP(sk2,sk3))) = true,
inference(step,[status(thm)],[t142310,t666]) ).
cnf(t667,plain,
or(not(neq(sk3,nil)),not(frontsegP(sk2,sk3))) = true,
inference(rw,[status(thm)],[t142311]) ).
cnf(t144625,plain,
or(not(neq(sk3,nil)),not(frontsegP(sk4,sk3))) = true,
inference(step,[status(thm)],[t667,t680]) ).
cnf(t16702,plain,
or(not(neq(sk3,nil)),not(frontsegP(sk4,sk3))) = true,
inference(orient,[status(thm)],[t144625]) ).
cnf(f143,axiom,
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).
fof(f143_nnf,plain,
! [U,V,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != W ),
inference(nnf_transformation,[status(thm)],[f143]) ).
fof(f143_sk,plain,
! [U,V,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != W ),
inference(skolemisation,[status(esa)],[f143_nnf]) ).
cnf(c143,plain,
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(esa)],[f143_sk]) ).
cnf(t171,plain,
ifeq(app(X1,X2),X3,ifeq(ssList(X2),true,ifeq(ssList(X1),true,ifeq(ssList(X3),true,frontsegP(X3,X1),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c143]) ).
cnf(t303,plain,
ifeq(app(X1,X2),X3,ifeq(ssList(X2),true,ifeq(ssList(X1),true,ifeq(ssList(X3),true,frontsegP(X3,X1),true),true),true),true) = true,
inference(orient,[status(thm)],[t171]) ).
cnf(t304,plain,
true = ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(app(X2,X1)),true,frontsegP(app(X2,X1),X2),true),true),true),
inference(cp,[status(thm)],[t303,t223]) ).
cnf(t139462,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(app(X2,X1)),true,frontsegP(app(X2,X1),X2),true),true),true) = true,
inference(orient,[status(thm)],[t304]) ).
cnf(f193,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f193_nnf,plain,
app(sk3,sk5) = sk4,
inference(nnf_transformation,[status(thm)],[f193]) ).
cnf(c193,plain,
app(sk3,sk5) = sk4,
inference(cnf_transformation,[status(esa)],[f193_nnf]) ).
cnf(t21,plain,
app(sk3,sk5) = sk4,
inference(equality_encoding,[status(esa)],[c193]) ).
cnf(t581,plain,
app(sk3,sk5) = sk4,
inference(orient,[status(thm)],[t21]) ).
cnf(t140415,plain,
true = ifeq(ssList(sk5),true,ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,frontsegP(app(sk3,sk5),sk3),true),true),true),
inference(cp,[status(thm)],[t139462,t581]) ).
cnf(f192,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f192_nnf,plain,
ssList(sk5),
inference(nnf_transformation,[status(thm)],[f192]) ).
cnf(c192,plain,
ssList(sk5),
inference(cnf_transformation,[status(esa)],[f192_nnf]) ).
cnf(t15,plain,
ssList(sk5) = true,
inference(equality_encoding,[status(esa)],[c192]) ).
cnf(t1238,plain,
ssList(sk5) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t146848,plain,
true = ifeq(true,true,ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,frontsegP(app(sk3,sk5),sk3),true),true),true),
inference(step,[status(thm)],[t140415,t1238]) ).
cnf(t146849,plain,
true = ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,frontsegP(app(sk3,sk5),sk3),true),true),
inference(step,[status(thm)],[t146848,t223]) ).
cnf(f187,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f187_nnf,plain,
ssList(sk3),
inference(nnf_transformation,[status(thm)],[f187]) ).
cnf(c187,plain,
ssList(sk3),
inference(cnf_transformation,[status(esa)],[f187_nnf]) ).
cnf(t13,plain,
ssList(sk3) = true,
inference(equality_encoding,[status(esa)],[c187]) ).
cnf(t862,plain,
ssList(sk3) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t146850,plain,
true = ifeq(true,true,ifeq(ssList(sk4),true,frontsegP(app(sk3,sk5),sk3),true),true),
inference(step,[status(thm)],[t146849,t862]) ).
cnf(t146851,plain,
true = ifeq(ssList(sk4),true,frontsegP(app(sk3,sk5),sk3),true),
inference(step,[status(thm)],[t146850,t223]) ).
cnf(t146852,plain,
true = ifeq(true,true,frontsegP(app(sk3,sk5),sk3),true),
inference(step,[status(thm)],[t146851,t1050]) ).
cnf(t146853,plain,
true = frontsegP(app(sk3,sk5),sk3),
inference(step,[status(thm)],[t146852,t223]) ).
cnf(t146854,plain,
true = frontsegP(sk4,sk3),
inference(step,[status(thm)],[t146853,t581]) ).
cnf(t140518,plain,
frontsegP(sk4,sk3) = true,
inference(orient,[status(thm)],[t146854]) ).
cnf(t146855,plain,
or(not(neq(sk3,nil)),not(true)) = true,
inference(step,[status(thm)],[t16702,t140518]) ).
cnf(t146856,plain,
or(not(neq(sk3,nil)),false) = true,
inference(step,[status(thm)],[t146855,t622]) ).
cnf(t146857,plain,
not(neq(sk3,nil)) = true,
inference(step,[status(thm)],[t146856,t265]) ).
cnf(t140529,plain,
not(neq(sk3,nil)) = true,
inference(rw,[status(thm)],[t146857]) ).
cnf(t140530,plain,
not(neq(sk3,nil)) = true,
inference(orient,[status(thm)],[t140529]) ).
cnf(t140531,plain,
false = ifeq(true,true,neq(sk3,nil),false),
inference(cp,[status(thm)],[t337,t140530]) ).
cnf(t146858,plain,
false = neq(sk3,nil),
inference(step,[status(thm)],[t140531,t223]) ).
cnf(t140532,plain,
neq(sk3,nil) = false,
inference(orient,[status(thm)],[t146858]) ).
cnf(t140533,plain,
true = ifeq(ssList(nil),true,ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),true),
inference(cp,[status(thm)],[t424,t140532]) ).
cnf(t146859,plain,
true = ifeq(true,true,ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),true),
inference(step,[status(thm)],[t140533,t686]) ).
cnf(t146860,plain,
true = ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),
inference(step,[status(thm)],[t146859,t223]) ).
cnf(t146861,plain,
true = ifeq(true,true,or(false,eq(sk3,nil)),true),
inference(step,[status(thm)],[t146860,t862]) ).
cnf(t146862,plain,
true = or(false,eq(sk3,nil)),
inference(step,[status(thm)],[t146861,t223]) ).
cnf(t146863,plain,
true = eq(sk3,nil),
inference(step,[status(thm)],[t146862,t266]) ).
cnf(t140536,plain,
eq(sk3,nil) = true,
inference(orient,[status(thm)],[t146863]) ).
cnf(t140537,plain,
nil = ifeq(true,true,sk3,nil),
inference(cp,[status(thm)],[t236,t140536]) ).
cnf(t146864,plain,
nil = sk3,
inference(step,[status(thm)],[t140537,t223]) ).
cnf(t140543,plain,
nil = sk3,
inference(orient,[status(thm)],[t146864]) ).
cnf(t146899,plain,
eq(sk4,sk3) = false,
inference(step,[status(thm)],[t9938,t140543]) ).
cnf(t140561,plain,
eq(sk4,sk3) = false,
inference(rw,[status(thm)],[t146899]) ).
cnf(f73,axiom,
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
fof(f73_nnf,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t80,plain,
ifeq(ssList(X1),true,app(nil,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t259,plain,
ifeq(ssList(X1),true,app(nil,X1),X1) = X1,
inference(orient,[status(thm)],[t80]) ).
cnf(t1245,plain,
sk5 = ifeq(true,true,app(nil,sk5),sk5),
inference(cp,[status(thm)],[t259,t1238]) ).
cnf(t142341,plain,
sk5 = app(nil,sk5),
inference(step,[status(thm)],[t1245,t223]) ).
cnf(t8910,plain,
app(nil,sk5) = sk5,
inference(orient,[status(thm)],[t142341]) ).
cnf(t146903,plain,
app(sk3,sk5) = sk5,
inference(step,[status(thm)],[t8910,t140543]) ).
cnf(t146904,plain,
sk4 = sk5,
inference(step,[status(thm)],[t146903,t581]) ).
cnf(t140565,plain,
sk4 = sk5,
inference(rw,[status(thm)],[t146904]) ).
cnf(t141921,plain,
sk4 = sk5,
inference(orient,[status(thm)],[t140565]) ).
cnf(t149321,plain,
eq(sk5,sk3) = false,
inference(step,[status(thm)],[t140561,t141921]) ).
cnf(f196,negated_conjecture,
( nil != sk3
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f196_nnf,plain,
( nil != sk3
| nil = sk4 ),
inference(nnf_transformation,[status(thm)],[f196]) ).
fof(f196_sk,plain,
( nil != sk3
| nil = sk4 ),
inference(skolemisation,[status(esa)],[f196_nnf]) ).
cnf(c196,plain,
( nil != sk3
| nil = sk4 ),
inference(cnf_transformation,[status(esa)],[f196_sk]) ).
cnf(t72,plain,
ifeq(nil,sk3,nil,sk4) = sk4,
inference(equality_encoding,[status(esa)],[c196]) ).
cnf(t336,plain,
ifeq(nil,sk3,nil,sk4) = sk4,
inference(orient,[status(thm)],[t72]) ).
cnf(t146925,plain,
ifeq(sk3,sk3,nil,sk4) = sk4,
inference(step,[status(thm)],[t336,t140543]) ).
cnf(t146926,plain,
nil = sk4,
inference(step,[status(thm)],[t146925,t223]) ).
cnf(t146927,plain,
sk3 = sk4,
inference(step,[status(thm)],[t146926,t140543]) ).
cnf(t140584,plain,
sk3 = sk4,
inference(rw,[status(thm)],[t146927]) ).
cnf(t148913,plain,
sk3 = sk5,
inference(step,[status(thm)],[t140584,t141921]) ).
cnf(t141927,plain,
sk3 = sk5,
inference(orient,[status(thm)],[t148913]) ).
cnf(t149322,plain,
eq(sk5,sk5) = false,
inference(step,[status(thm)],[t149321,t141927]) ).
cnf(t22,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t624,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t149323,plain,
true = false,
inference(step,[status(thm)],[t149322,t624]) ).
cnf(t142228,plain,
false = true,
inference(orient,[status(thm)],[t149323]) ).
cnf(f10,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
fof(f10_nnf,plain,
~ singletonP(nil),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ singletonP(nil),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f53,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
fof(f53_nnf,plain,
skac3 != skac2,
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
skac3 != skac2,
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
skac3 != skac2,
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(f62,axiom,
( ~ ssItem(U)
| ~ lt(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
fof(f62_nnf,plain,
! [U] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [U] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c62,plain,
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
cnf(f70,axiom,
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
fof(f70_nnf,plain,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c70,plain,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(f97,axiom,
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
fof(f97_nnf,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
inference(nnf_transformation,[status(thm)],[f97]) ).
fof(f97_sk,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
inference(skolemisation,[status(esa)],[f97_nnf]) ).
cnf(c97,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(esa)],[f97_sk]) ).
cnf(f98,axiom,
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
fof(f98_nnf,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
inference(nnf_transformation,[status(thm)],[f98]) ).
fof(f98_sk,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
inference(skolemisation,[status(esa)],[f98_nnf]) ).
cnf(c98,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f98_sk]) ).
cnf(f109,axiom,
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
fof(f109_nnf,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c109,plain,
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(f110,axiom,
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
fof(f110_nnf,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f110]) ).
fof(f110_sk,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f110_nnf]) ).
cnf(c110,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f110_sk]) ).
cnf(f113,axiom,
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
fof(f113_nnf,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(f116,axiom,
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
fof(f116_nnf,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c116,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
cnf(f178,axiom,
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause179) ).
fof(f178_nnf,plain,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
inference(nnf_transformation,[status(thm)],[f178]) ).
fof(f178_sk,plain,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
inference(skolemisation,[status(esa)],[f178_nnf]) ).
cnf(c178,plain,
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
inference(cnf_transformation,[status(esa)],[f178_sk]) ).
cnf(f184,axiom,
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause185) ).
fof(f184_nnf,plain,
! [U,V,W,X,Y,Z] :
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
inference(nnf_transformation,[status(thm)],[f184]) ).
fof(f184_sk,plain,
! [U,V,W,X,Y,Z] :
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
inference(skolemisation,[status(esa)],[f184_nnf]) ).
cnf(c184,plain,
( ~ ssList(X5)
| ~ cyclefreeP(X5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f184_sk]) ).
cnf(f195,negated_conjecture,
( ~ leq(C,A)
| app(D,cons(C,nil)) != sk3
| ~ ssList(D)
| ~ ssItem(C)
| app(cons(A,nil),B) != sk5
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f195_nnf,plain,
! [A,B,C,D] :
( ~ leq(C,A)
| app(D,cons(C,nil)) != sk3
| ~ ssList(D)
| ~ ssItem(C)
| app(cons(A,nil),B) != sk5
| ~ ssList(B)
| ~ ssItem(A) ),
inference(nnf_transformation,[status(thm)],[f195]) ).
fof(f195_sk,plain,
! [A,B,C,D] :
( ~ leq(C,A)
| app(D,cons(C,nil)) != sk3
| ~ ssList(D)
| ~ ssItem(C)
| app(cons(A,nil),B) != sk5
| ~ ssList(B)
| ~ ssItem(A) ),
inference(skolemisation,[status(esa)],[f195_nnf]) ).
cnf(c195,plain,
( ~ leq(X2,X0)
| app(X3,cons(X2,nil)) != sk3
| ~ ssList(X3)
| ~ ssItem(X2)
| app(cons(X0,nil),X1) != sk5
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f195_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c10,c53,c62,c70,c97,c98,c109,c110,c113,c114,c116,c178,c184,c195,c197]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t142228]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC104-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.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 : Thu Sep 24 16:24:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 106.30/15.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.30/15.63 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------