%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWW413-1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 03:27:04 PM UTC 2026
% Result : Unsatisfiable 3.85s 1.05s
% Output : Proof 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 83 ( 79 unt; 0 def)
% Number of atoms : 91 ( 67 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 42 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 80 ( 12 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f13,hypothesis,
x3 != x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_3) ).
fof(f13_nnf,plain,
x3 != x2,
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
x3 != x2,
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
x3 != x2,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t4,plain,
eq(x3,x2) = false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t147,plain,
eq(x3,x2) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t21,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t39,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t21]) ).
cnf(f7,axiom,
( heap(sep(lseg(X,Z),Sigma))
| X = Y
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unfolding_2) ).
fof(f7_nnf,plain,
! [X,Y,Z,Sigma] :
( heap(sep(lseg(X,Z),Sigma))
| X = Y
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,Z,Sigma] :
( heap(sep(lseg(X,Z),Sigma))
| X = Y
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( heap(sep(lseg(X0,X2),X3))
| X0 = X1
| ~ heap(sep(next(X0,X1),sep(lseg(X1,X2),X3))) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t32,plain,
ifeq(heap(sep(next(X1,X2),sep(lseg(X2,X3),X4))),true,or(eq(X1,X2),heap(sep(lseg(X1,X3),X4))),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t62,plain,
ifeq(heap(sep(next(X1,X2),sep(lseg(X2,X3),X4))),true,or(eq(X1,X2),heap(sep(lseg(X1,X3),X4))),true) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(f17,hypothesis,
heap(sep(lseg(x3,nil),sep(next(x2,x3),emp))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_7) ).
fof(f17_nnf,plain,
heap(sep(lseg(x3,nil),sep(next(x2,x3),emp))),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
heap(sep(lseg(x3,nil),sep(next(x2,x3),emp))),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(t23,plain,
heap(sep(lseg(x3,nil),sep(next(x2,x3),emp))) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t42,plain,
heap(sep(lseg(x3,nil),sep(next(x2,x3),emp))) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t105,plain,
heap(sep(lseg(x3,nil),sep(next(x2,x3),emp))) = true,
inference(rw,[status(thm)],[t42]) ).
cnf(f0,axiom,
sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_commutative) ).
fof(f0_nnf,plain,
! [S,T,Sigma] : sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [S,T,Sigma] : sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
sep(X0,sep(X1,X2)) = sep(X1,sep(X0,X2)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t22,plain,
sep(X1,sep(X2,X3)) = sep(X2,sep(X1,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t81,plain,
sep(X1,sep(X2,X3)) = sep(X2,sep(X1,X3)),
inference(orient,[status(thm)],[t22]) ).
cnf(t217,plain,
heap(sep(next(x2,x3),sep(lseg(x3,nil),emp))) = true,
inference(step,[status(thm)],[t105,t81]) ).
cnf(t175,plain,
heap(sep(next(x2,x3),sep(lseg(x3,nil),emp))) = true,
inference(orient,[status(thm)],[t217]) ).
cnf(t176,plain,
true = ifeq(true,true,or(eq(x2,x3),heap(sep(lseg(x2,nil),emp))),true),
inference(cp,[status(thm)],[t62,t175]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t36,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t218,plain,
true = or(eq(x2,x3),heap(sep(lseg(x2,nil),emp))),
inference(step,[status(thm)],[t176,t36]) ).
cnf(f18,negated_conjecture,
~ heap(sep(lseg(x2,nil),emp)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_1) ).
fof(f18_nnf,plain,
~ heap(sep(lseg(x2,nil),emp)),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ heap(sep(lseg(x2,nil),emp)),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
~ heap(sep(lseg(x2,nil),emp)),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t19,plain,
heap(sep(lseg(x2,nil),emp)) = false,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t106,plain,
heap(sep(lseg(x2,nil),emp)) = false,
inference(orient,[status(thm)],[t19]) ).
cnf(t219,plain,
true = or(eq(x2,x3),false),
inference(step,[status(thm)],[t218,t106]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t40,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t220,plain,
true = eq(x2,x3),
inference(step,[status(thm)],[t219,t40]) ).
cnf(t177,plain,
eq(x2,x3) = true,
inference(orient,[status(thm)],[t220]) ).
cnf(t178,plain,
x3 = ifeq(true,true,x2,x3),
inference(cp,[status(thm)],[t39,t177]) ).
cnf(t221,plain,
x3 = x2,
inference(step,[status(thm)],[t178,t36]) ).
cnf(t183,plain,
x2 = x3,
inference(orient,[status(thm)],[t221]) ).
cnf(t226,plain,
eq(x3,x3) = false,
inference(step,[status(thm)],[t147,t183]) ).
cnf(t0,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t74,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t227,plain,
true = false,
inference(step,[status(thm)],[t226,t74]) ).
cnf(t186,plain,
true = false,
inference(rw,[status(thm)],[t227]) ).
cnf(t196,plain,
false = true,
inference(orient,[status(thm)],[t186]) ).
cnf(f2,axiom,
~ heap(sep(next(nil,Y),Sigma)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_1) ).
fof(f2_nnf,plain,
! [Y,Sigma] : ~ heap(sep(next(nil,Y),Sigma)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Y,Sigma] : ~ heap(sep(next(nil,Y),Sigma)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ heap(sep(next(nil,X0),X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f4,axiom,
~ heap(sep(next(X,Y),sep(next(X,Z),Sigma))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_3) ).
fof(f4_nnf,plain,
! [X,Y,Z,Sigma] : ~ heap(sep(next(X,Y),sep(next(X,Z),Sigma))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z,Sigma] : ~ heap(sep(next(X,Y),sep(next(X,Z),Sigma))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ heap(sep(next(X0,X1),sep(next(X0,X2),X3))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f11,hypothesis,
nil != x1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_1) ).
fof(f11_nnf,plain,
nil != x1,
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
nil != x1,
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
nil != x1,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(f12,hypothesis,
nil != x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_2) ).
fof(f12_nnf,plain,
nil != x2,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
nil != x2,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
nil != x2,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(f14,hypothesis,
x4 != x1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_4) ).
fof(f14_nnf,plain,
x4 != x1,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
x4 != x1,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
x4 != x1,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(f15,hypothesis,
x4 != x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_5) ).
fof(f15_nnf,plain,
x4 != x2,
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
x4 != x2,
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
x4 != x2,
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(f16,hypothesis,
x1 != x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_6) ).
fof(f16_nnf,plain,
x1 != x2,
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
x1 != x2,
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
x1 != x2,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c4,c11,c12,c13,c14,c15,c16,c18]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t196]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW413-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 22:18:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.85/1.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.85/1.05 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------