%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN204-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 03:34:04 PM UTC 2026
% Result : Unsatisfiable 7.49s 1.47s
% Output : Proof 7.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 115 ( 67 unt; 0 def)
% Number of atoms : 215 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 206 ( 106 ~; 100 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 162 ( 35 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f162,axiom,
( ~ p0(I,I)
| s1(I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_125) ).
fof(f162_nnf,plain,
! [I] :
( ~ p0(I,I)
| s1(I) ),
inference(nnf_transformation,[status(thm)],[f162]) ).
fof(f162_sk,plain,
! [I] :
( ~ p0(I,I)
| s1(I) ),
inference(skolemisation,[status(esa)],[f162_nnf]) ).
cnf(c162,plain,
( ~ p0(X0,X0)
| s1(X0) ),
inference(cnf_transformation,[status(esa)],[f162_sk]) ).
cnf(hi160,axiom,
ifeq(p0(X0,X0),true,s1(X0),true) = true,
inference(equality_encoding,[status(esa)],[c162]) ).
cnf(f13,axiom,
p0(b,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
fof(f13_nnf,plain,
! [X] : p0(b,X),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : p0(b,X),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
p0(b,X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
p0(b,X0) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h26,plain,
s1(b) = true,
inference(hyper_resolution,[status(thm)],[hi160,hi13]) ).
cnf(f163,axiom,
( ~ s1(H)
| ~ q0(F,G)
| s1(F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_126) ).
fof(f163_nnf,plain,
! [F,G,H] :
( ~ s1(H)
| ~ q0(F,G)
| s1(F) ),
inference(nnf_transformation,[status(thm)],[f163]) ).
fof(f163_sk,plain,
! [F,G,H] :
( ~ s1(H)
| ~ q0(F,G)
| s1(F) ),
inference(skolemisation,[status(esa)],[f163_nnf]) ).
cnf(c163,plain,
( ~ s1(X2)
| ~ q0(X0,X1)
| s1(X0) ),
inference(cnf_transformation,[status(esa)],[f163_sk]) ).
cnf(hi161,axiom,
ifeq(q0(X0,X1),true,ifeq(s1(X2),true,s1(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c163]) ).
cnf(f16,axiom,
q0(X,d),
file('/export/starexec/sandbox/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(h117,plain,
s1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi16,h26]) ).
cnf(f112,axiom,
( ~ p0(b,a)
| p1(a,a,a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_075) ).
fof(f112_nnf,plain,
( ~ p0(b,a)
| p1(a,a,a) ),
inference(nnf_transformation,[status(thm)],[f112]) ).
fof(f112_sk,plain,
( ~ p0(b,a)
| p1(a,a,a) ),
inference(skolemisation,[status(esa)],[f112_nnf]) ).
cnf(c112,plain,
( ~ p0(b,a)
| p1(a,a,a) ),
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(hi111,axiom,
ifeq(p0(b,a),true,p1(a,a,a),true) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(h31,plain,
p1(a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi111,hi13]) ).
cnf(f214,axiom,
( ~ p1(E,E,E)
| ~ k0(F)
| q2(E,F,F) ),
file('/export/starexec/sandbox/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(f31,axiom,
k0(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
fof(f31_nnf,plain,
k0(b),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
k0(b),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi31,axiom,
k0(b) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(h177,plain,
q2(a,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi211,hi31,h31]) ).
cnf(f87,axiom,
( ~ p0(b,E)
| ~ l0(D)
| ~ s0(b)
| n1(D,E,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_050) ).
fof(f87_nnf,plain,
! [D,E] :
( ~ p0(b,E)
| ~ l0(D)
| ~ s0(b)
| n1(D,E,D) ),
inference(nnf_transformation,[status(thm)],[f87]) ).
fof(f87_sk,plain,
! [D,E] :
( ~ p0(b,E)
| ~ l0(D)
| ~ s0(b)
| n1(D,E,D) ),
inference(skolemisation,[status(esa)],[f87_nnf]) ).
cnf(c87,plain,
( ~ p0(b,X1)
| ~ l0(X0)
| ~ s0(b)
| n1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(hi86,axiom,
ifeq(s0(b),true,ifeq(l0(X0),true,ifeq(p0(b,X1),true,n1(X0,X1,X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c87]) ).
cnf(f4,axiom,
s0(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f4_nnf,plain,
s0(b),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
s0(b),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,axiom,
s0(b) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f19,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
fof(f19_nnf,plain,
l0(a),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
l0(a),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
l0(a) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h37,plain,
n1(a,V0,a) = true,
inference(hyper_resolution,[status(thm)],[hi86,hi4,hi19,hi13]) ).
cnf(f39,axiom,
( ~ n0(H,G)
| l1(G,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_002) ).
fof(f39_nnf,plain,
! [G,H] :
( ~ n0(H,G)
| l1(G,G) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [G,H] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( ~ n0(X1,X0)
| l1(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi39,axiom,
ifeq(n0(X0,X1),true,l1(X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(f36,axiom,
n0(b,a),
file('/export/starexec/sandbox/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(h109,plain,
l1(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi36]) ).
cnf(f91,axiom,
( ~ n1(E,F,E)
| ~ l1(G,E)
| ~ l0(G)
| n1(E,F,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_054) ).
fof(f91_nnf,plain,
! [E,F,G] :
( ~ n1(E,F,E)
| ~ l1(G,E)
| ~ l0(G)
| n1(E,F,F) ),
inference(nnf_transformation,[status(thm)],[f91]) ).
fof(f91_sk,plain,
! [E,F,G] :
( ~ n1(E,F,E)
| ~ l1(G,E)
| ~ l0(G)
| n1(E,F,F) ),
inference(skolemisation,[status(esa)],[f91_nnf]) ).
cnf(c91,plain,
( ~ n1(X0,X1,X0)
| ~ l1(X2,X0)
| ~ l0(X2)
| n1(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f91_sk]) ).
cnf(hi90,axiom,
ifeq(l0(X0),true,ifeq(l1(X0,X1),true,ifeq(n1(X1,X2,X1),true,n1(X1,X2,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(h248,plain,
n1(a,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi90,hi19,h109,h37]) ).
cnf(f106,axiom,
( ~ p0(C,B)
| p1(B,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_069) ).
fof(f106_nnf,plain,
! [B,C] :
( ~ p0(C,B)
| p1(B,B,C) ),
inference(nnf_transformation,[status(thm)],[f106]) ).
fof(f106_sk,plain,
! [B,C] :
( ~ p0(C,B)
| p1(B,B,C) ),
inference(skolemisation,[status(esa)],[f106_nnf]) ).
cnf(c106,plain,
( ~ p0(X1,X0)
| p1(X0,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f106_sk]) ).
cnf(hi105,axiom,
ifeq(p0(X0,X1),true,p1(X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c106]) ).
cnf(h33,plain,
p1(V0,V0,b) = true,
inference(hyper_resolution,[status(thm)],[hi105,hi13]) ).
cnf(f108,axiom,
( ~ s0(b)
| ~ p1(I,A,H)
| ~ l0(J)
| p1(H,I,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_071) ).
fof(f108_nnf,plain,
! [H,I,J,A] :
( ~ s0(b)
| ~ p1(I,A,H)
| ~ l0(J)
| p1(H,I,H) ),
inference(nnf_transformation,[status(thm)],[f108]) ).
fof(f108_sk,plain,
! [H,I,J,A] :
( ~ s0(b)
| ~ p1(I,A,H)
| ~ l0(J)
| p1(H,I,H) ),
inference(skolemisation,[status(esa)],[f108_nnf]) ).
cnf(c108,plain,
( ~ s0(b)
| ~ p1(X1,X3,X0)
| ~ l0(X2)
| p1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f108_sk]) ).
cnf(hi107,axiom,
ifeq(l0(X0),true,ifeq(p1(X1,X2,X3),true,ifeq(s0(b),true,p1(X3,X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c108]) ).
cnf(f23,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
fof(f23_nnf,plain,
l0(c),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
l0(c),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,axiom,
l0(c) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h183,plain,
p1(b,V0,b) = true,
inference(hyper_resolution,[status(thm)],[hi107,hi23,h33,hi4]) ).
cnf(f219,axiom,
( ~ q2(G,H,F)
| ~ n1(G,F,H)
| ~ p1(F,F,H)
| q2(F,G,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_182) ).
fof(f219_nnf,plain,
! [F,G,H] :
( ~ q2(G,H,F)
| ~ n1(G,F,H)
| ~ p1(F,F,H)
| q2(F,G,F) ),
inference(nnf_transformation,[status(thm)],[f219]) ).
fof(f219_sk,plain,
! [F,G,H] :
( ~ q2(G,H,F)
| ~ n1(G,F,H)
| ~ p1(F,F,H)
| q2(F,G,F) ),
inference(skolemisation,[status(esa)],[f219_nnf]) ).
cnf(c219,plain,
( ~ q2(X1,X2,X0)
| ~ n1(X1,X0,X2)
| ~ p1(X0,X0,X2)
| q2(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f219_sk]) ).
cnf(hi216,axiom,
ifeq(p1(X0,X0,X1),true,ifeq(n1(X2,X0,X1),true,ifeq(q2(X2,X1,X0),true,q2(X0,X2,X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c219]) ).
cnf(h510,plain,
q2(b,a,b) = true,
inference(hyper_resolution,[status(thm)],[hi216,h183,h248,h177]) ).
cnf(f226,axiom,
( ~ s1(b)
| ~ q2(b,H,b)
| s2(H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_189) ).
fof(f226_nnf,plain,
! [H] :
( ~ s1(b)
| ~ q2(b,H,b)
| s2(H) ),
inference(nnf_transformation,[status(thm)],[f226]) ).
fof(f226_sk,plain,
! [H] :
( ~ s1(b)
| ~ q2(b,H,b)
| s2(H) ),
inference(skolemisation,[status(esa)],[f226_nnf]) ).
cnf(c226,plain,
( ~ s1(b)
| ~ q2(b,X0,b)
| s2(X0) ),
inference(cnf_transformation,[status(esa)],[f226_sk]) ).
cnf(hi223,axiom,
ifeq(q2(b,X0,b),true,ifeq(s1(b),true,s2(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c226]) ).
cnf(h736,plain,
s2(a) = true,
inference(hyper_resolution,[status(thm)],[hi223,h510,h117]) ).
cnf(f310,axiom,
( ~ m0(A,B,J)
| ~ s2(I)
| ~ q2(A,I,A)
| s3(I,J) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_273) ).
fof(f310_nnf,plain,
! [I,J,A,B] :
( ~ m0(A,B,J)
| ~ s2(I)
| ~ q2(A,I,A)
| s3(I,J) ),
inference(nnf_transformation,[status(thm)],[f310]) ).
fof(f310_sk,plain,
! [I,J,A,B] :
( ~ m0(A,B,J)
| ~ s2(I)
| ~ q2(A,I,A)
| s3(I,J) ),
inference(skolemisation,[status(esa)],[f310_nnf]) ).
cnf(c310,plain,
( ~ m0(X2,X3,X1)
| ~ s2(X0)
| ~ q2(X2,X0,X2)
| s3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f310_sk]) ).
cnf(hi305,axiom,
ifeq(q2(X0,X1,X0),true,ifeq(s2(X1),true,ifeq(m0(X0,X2,X3),true,s3(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c310]) ).
cnf(f18,axiom,
m0(X,d,Y),
file('/export/starexec/sandbox/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(t43,plain,
s3(a,X1) = true,
inference(hyper_resolution,[status(thm)],[hi305,h510,h736,hi18]) ).
cnf(t66,plain,
s3(a,X1) = true,
inference(orient,[status(thm)],[t43]) ).
cnf(f368,negated_conjecture,
~ s3(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ s3(a,c),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ s3(a,c),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ s3(a,c),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
s3(a,c) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t66]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN204-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n008.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 00:30:23 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.49/1.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.49/1.47 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------