%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN215-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 03:34:05 PM UTC 2026
% Result : Unsatisfiable 3.54s 0.93s
% Output : Proof 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 118 ( 66 unt; 0 def)
% Number of atoms : 202 ( 38 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 174 ( 90 ~; 84 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 190 ( 51 sgn 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f103,axiom,
( ~ n0(H,G)
| p1(G,G,G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_066) ).
fof(f103_nnf,plain,
! [G,H] :
( ~ n0(H,G)
| p1(G,G,G) ),
inference(nnf_transformation,[status(thm)],[f103]) ).
fof(f103_sk,plain,
! [G,H] :
( ~ n0(H,G)
| p1(G,G,G) ),
inference(skolemisation,[status(esa)],[f103_nnf]) ).
cnf(c103,plain,
( ~ n0(X1,X0)
| p1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f103_sk]) ).
cnf(hi102,axiom,
ifeq(n0(X0,X1),true,p1(X1,X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c103]) ).
cnf(f33,axiom,
n0(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
fof(f33_nnf,plain,
n0(c,d),
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c33,plain,
n0(c,d),
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(hi33,axiom,
n0(c,d) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(h13,plain,
p1(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi102,hi33]) ).
cnf(f27,axiom,
k0(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
fof(f27_nnf,plain,
k0(e),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
k0(e),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi27,axiom,
k0(e) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h12,plain,
k0(e) = true,
inference(hyper_resolution,[status(thm)],[hi27]) ).
cnf(f214,axiom,
( ~ p1(E,E,E)
| ~ k0(F)
| q2(E,F,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_177) ).
fof(f214_nnf,plain,
! [E,F] :
( ~ p1(E,E,E)
| ~ k0(F)
| q2(E,F,F) ),
inference(nnf_transformation,[status(thm)],[f214]) ).
fof(f214_sk,plain,
! [E,F] :
( ~ p1(E,E,E)
| ~ k0(F)
| q2(E,F,F) ),
inference(skolemisation,[status(esa)],[f214_nnf]) ).
cnf(c214,plain,
( ~ p1(X0,X0,X0)
| ~ k0(X1)
| q2(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f214_sk]) ).
cnf(hi211,axiom,
ifeq(k0(X0),true,ifeq(p1(X1,X1,X1),true,q2(X1,X0,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c214]) ).
cnf(h17,plain,
q2(d,e,e) = true,
inference(hyper_resolution,[status(thm)],[hi211,h12,h13]) ).
cnf(f292,axiom,
( ~ n0(I,G)
| ~ q2(I,G,H)
| q3(G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_255) ).
fof(f292_nnf,plain,
! [G,H,I] :
( ~ n0(I,G)
| ~ q2(I,G,H)
| q3(G,H) ),
inference(nnf_transformation,[status(thm)],[f292]) ).
fof(f292_sk,plain,
! [G,H,I] :
( ~ n0(I,G)
| ~ q2(I,G,H)
| q3(G,H) ),
inference(skolemisation,[status(esa)],[f292_nnf]) ).
cnf(c292,plain,
( ~ n0(X2,X0)
| ~ q2(X2,X0,X1)
| q3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f292_sk]) ).
cnf(hi287,axiom,
ifeq(q2(X0,X1,X2),true,ifeq(n0(X0,X1),true,q3(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c292]) ).
cnf(f2,axiom,
n0(d,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f2_nnf,plain,
n0(d,e),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
n0(d,e),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi2,axiom,
n0(d,e) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h18,plain,
q3(e,e) = true,
inference(hyper_resolution,[status(thm)],[hi287,h17,hi2]) ).
cnf(f129,axiom,
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_092) ).
fof(f129_nnf,plain,
! [J,A,B,C] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(nnf_transformation,[status(thm)],[f129]) ).
fof(f129_sk,plain,
! [J,A,B,C] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(skolemisation,[status(esa)],[f129_nnf]) ).
cnf(c129,plain,
( ~ p0(X3,X0)
| ~ n0(X2,X1)
| q1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f129_sk]) ).
cnf(hi127,axiom,
ifeq(n0(X0,X1),true,ifeq(p0(X2,X3),true,q1(X3,X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c129]) ).
cnf(f36,axiom,
n0(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
fof(f36_nnf,plain,
n0(b,a),
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c36,plain,
n0(b,a),
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
cnf(hi36,axiom,
n0(b,a) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(f9,axiom,
p0(b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
fof(f9_nnf,plain,
p0(b,d),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
p0(b,d),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(hi9,axiom,
p0(b,d) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h14,plain,
q1(d,a,d) = true,
inference(hyper_resolution,[status(thm)],[hi127,hi36,hi9]) ).
cnf(f178,axiom,
( ~ q1(B,a,B)
| p2(B,a,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_141) ).
fof(f178_nnf,plain,
! [B] :
( ~ q1(B,a,B)
| p2(B,a,B) ),
inference(nnf_transformation,[status(thm)],[f178]) ).
fof(f178_sk,plain,
! [B] :
( ~ q1(B,a,B)
| p2(B,a,B) ),
inference(skolemisation,[status(esa)],[f178_nnf]) ).
cnf(c178,plain,
( ~ q1(X0,a,X0)
| p2(X0,a,X0) ),
inference(cnf_transformation,[status(esa)],[f178_sk]) ).
cnf(hi175,axiom,
ifeq(q1(X0,a,X0),true,p2(X0,a,X0),true) = true,
inference(equality_encoding,[status(esa)],[c178]) ).
cnf(h15,plain,
p2(d,a,d) = true,
inference(hyper_resolution,[status(thm)],[hi175,h14]) ).
cnf(f277,axiom,
( ~ p2(E,F,D)
| n3(D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_240) ).
fof(f277_nnf,plain,
! [D,E,F] :
( ~ p2(E,F,D)
| n3(D) ),
inference(nnf_transformation,[status(thm)],[f277]) ).
fof(f277_sk,plain,
! [D,E,F] :
( ~ p2(E,F,D)
| n3(D) ),
inference(skolemisation,[status(esa)],[f277_nnf]) ).
cnf(c277,plain,
( ~ p2(X1,X2,X0)
| n3(X0) ),
inference(cnf_transformation,[status(esa)],[f277_sk]) ).
cnf(hi272,axiom,
ifeq(p2(X0,X1,X2),true,n3(X2),true) = true,
inference(equality_encoding,[status(esa)],[c277]) ).
cnf(h16,plain,
n3(d) = true,
inference(hyper_resolution,[status(thm)],[hi272,h15]) ).
cnf(f335,axiom,
( ~ p0(J,G)
| ~ q3(H,I)
| ~ n3(G)
| r4(G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_298) ).
fof(f335_nnf,plain,
! [G,H,I,J] :
( ~ p0(J,G)
| ~ q3(H,I)
| ~ n3(G)
| r4(G) ),
inference(nnf_transformation,[status(thm)],[f335]) ).
fof(f335_sk,plain,
! [G,H,I,J] :
( ~ p0(J,G)
| ~ q3(H,I)
| ~ n3(G)
| r4(G) ),
inference(skolemisation,[status(esa)],[f335_nnf]) ).
cnf(c335,plain,
( ~ p0(X3,X0)
| ~ q3(X1,X2)
| ~ n3(X0)
| r4(X0) ),
inference(cnf_transformation,[status(esa)],[f335_sk]) ).
cnf(hi328,axiom,
ifeq(n3(X0),true,ifeq(q3(X1,X2),true,ifeq(p0(X3,X0),true,r4(X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c335]) ).
cnf(h19,plain,
r4(d) = true,
inference(hyper_resolution,[status(thm)],[hi328,h16,h18,hi9]) ).
cnf(h8,plain,
q1(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi127,hi33,hi9]) ).
cnf(f166,axiom,
( ~ q1(A,J,J)
| k2(J,J) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_129) ).
fof(f166_nnf,plain,
! [J,A] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(nnf_transformation,[status(thm)],[f166]) ).
fof(f166_sk,plain,
! [J,A] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(skolemisation,[status(esa)],[f166_nnf]) ).
cnf(c166,plain,
( ~ q1(X1,X0,X0)
| k2(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f166_sk]) ).
cnf(hi164,axiom,
ifeq(q1(X0,X1,X1),true,k2(X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c166]) ).
cnf(h9,plain,
k2(d,d) = true,
inference(hyper_resolution,[status(thm)],[hi164,h8]) ).
cnf(f73,axiom,
( ~ m0(b,B,A)
| n1(A,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_036) ).
fof(f73_nnf,plain,
! [A,B] :
( ~ m0(b,B,A)
| n1(A,A,B) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B] :
( ~ m0(b,B,A)
| n1(A,A,B) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( ~ m0(b,X1,X0)
| n1(X0,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(hi73,axiom,
ifeq(m0(b,X0,X1),true,n1(X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(f18,axiom,
m0(X,d,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
fof(f18_nnf,plain,
! [X,Y] : m0(X,d,Y),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y] : m0(X,d,Y),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
m0(X0,d,X1),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
m0(X0,d,X1) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h6,plain,
n1(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi73,hi18]) ).
cnf(f215,axiom,
( ~ n1(C,B,D)
| ~ q0(C,B)
| q2(B,B,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_178) ).
fof(f215_nnf,plain,
! [B,C,D] :
( ~ n1(C,B,D)
| ~ q0(C,B)
| q2(B,B,B) ),
inference(nnf_transformation,[status(thm)],[f215]) ).
fof(f215_sk,plain,
! [B,C,D] :
( ~ n1(C,B,D)
| ~ q0(C,B)
| q2(B,B,B) ),
inference(skolemisation,[status(esa)],[f215_nnf]) ).
cnf(c215,plain,
( ~ n1(X1,X0,X2)
| ~ q0(X1,X0)
| q2(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f215_sk]) ).
cnf(hi212,axiom,
ifeq(q0(X0,X1),true,ifeq(n1(X0,X1,X2),true,q2(X1,X1,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c215]) ).
cnf(f16,axiom,
q0(X,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
fof(f16_nnf,plain,
! [X] : q0(X,d),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X] : q0(X,d),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
q0(X0,d),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
q0(X0,d) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h7,plain,
q2(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi212,hi16,h6]) ).
cnf(f278,axiom,
( ~ k2(D,E)
| ~ q2(F,d,C)
| p3(C,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_241) ).
fof(f278_nnf,plain,
! [C,D,E,F] :
( ~ k2(D,E)
| ~ q2(F,d,C)
| p3(C,D,E) ),
inference(nnf_transformation,[status(thm)],[f278]) ).
fof(f278_sk,plain,
! [C,D,E,F] :
( ~ k2(D,E)
| ~ q2(F,d,C)
| p3(C,D,E) ),
inference(skolemisation,[status(esa)],[f278_nnf]) ).
cnf(c278,plain,
( ~ k2(X1,X2)
| ~ q2(X3,d,X0)
| p3(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f278_sk]) ).
cnf(hi273,axiom,
ifeq(q2(X0,d,X1),true,ifeq(k2(X2,X3),true,p3(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c278]) ).
cnf(h10,plain,
p3(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi273,h7,h9]) ).
cnf(f314,axiom,
( ~ p3(A,B,J)
| l4(J) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_277) ).
fof(f314_nnf,plain,
! [J,A,B] :
( ~ p3(A,B,J)
| l4(J) ),
inference(nnf_transformation,[status(thm)],[f314]) ).
fof(f314_sk,plain,
! [J,A,B] :
( ~ p3(A,B,J)
| l4(J) ),
inference(skolemisation,[status(esa)],[f314_nnf]) ).
cnf(c314,plain,
( ~ p3(X1,X2,X0)
| l4(X0) ),
inference(cnf_transformation,[status(esa)],[f314_sk]) ).
cnf(hi308,axiom,
ifeq(p3(X0,X1,X2),true,l4(X2),true) = true,
inference(equality_encoding,[status(esa)],[c314]) ).
cnf(h11,plain,
l4(d) = true,
inference(hyper_resolution,[status(thm)],[hi308,h10]) ).
cnf(f366,axiom,
( ~ r4(I)
| ~ l4(H)
| s5(H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_329) ).
fof(f366_nnf,plain,
! [H,I] :
( ~ r4(I)
| ~ l4(H)
| s5(H) ),
inference(nnf_transformation,[status(thm)],[f366]) ).
fof(f366_sk,plain,
! [H,I] :
( ~ r4(I)
| ~ l4(H)
| s5(H) ),
inference(skolemisation,[status(esa)],[f366_nnf]) ).
cnf(c366,plain,
( ~ r4(X1)
| ~ l4(X0)
| s5(X0) ),
inference(cnf_transformation,[status(esa)],[f366_sk]) ).
cnf(hi359,axiom,
ifeq(l4(X0),true,ifeq(r4(X1),true,s5(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c366]) ).
cnf(t0,plain,
s5(d) = true,
inference(hyper_resolution,[status(thm)],[hi359,h11,h19]) ).
cnf(t40,plain,
s5(d) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f368,negated_conjecture,
~ s5(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ s5(d),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ s5(d),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ s5(d),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
s5(d) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t40]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN215-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n016.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 00:36:58 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.54/0.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.54/0.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------