%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN205-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 6.46s 1.34s
% Output : Proof 6.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 123 ( 75 unt; 0 def)
% Number of atoms : 223 ( 37 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 : 173 ( 36 sgn 66 !; 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(h34,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(h51,plain,
s1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi16,h34]) ).
cnf(f122,axiom,
( ~ p0(C,B)
| p1(B,B,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_085) ).
fof(f122_nnf,plain,
! [B,C] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(nnf_transformation,[status(thm)],[f122]) ).
fof(f122_sk,plain,
! [B,C] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(skolemisation,[status(esa)],[f122_nnf]) ).
cnf(c122,plain,
( ~ p0(X1,X0)
| p1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f122_sk]) ).
cnf(hi120,axiom,
ifeq(p0(X0,X1),true,p1(X1,X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h41,plain,
p1(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi120,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(h188,plain,
q2(V0,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi211,hi31,h41]) ).
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(h44,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(h81,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(h198,plain,
n1(a,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi90,hi19,h81,h44]) ).
cnf(f100,axiom,
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_063) ).
fof(f100_nnf,plain,
! [D,E] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
inference(nnf_transformation,[status(thm)],[f100]) ).
fof(f100_sk,plain,
! [D,E] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
inference(skolemisation,[status(esa)],[f100_nnf]) ).
cnf(c100,plain,
( ~ k0(X1)
| ~ n0(d,X0)
| p1(X0,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f100_sk]) ).
cnf(hi99,axiom,
ifeq(n0(d,X0),true,ifeq(k0(X1),true,p1(X0,X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c100]) ).
cnf(f6,axiom,
n0(d,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f6_nnf,plain,
n0(d,b),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
n0(d,b),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(hi6,axiom,
n0(d,b) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f27,axiom,
k0(e),
file('/export/starexec/sandbox/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(h28,plain,
p1(b,b,e) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi6,hi27]) ).
cnf(f119,axiom,
( ~ p1(J,H,A)
| ~ m0(J,H,A)
| p1(H,I,J) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_082) ).
fof(f119_nnf,plain,
! [H,I,J,A] :
( ~ p1(J,H,A)
| ~ m0(J,H,A)
| p1(H,I,J) ),
inference(nnf_transformation,[status(thm)],[f119]) ).
fof(f119_sk,plain,
! [H,I,J,A] :
( ~ p1(J,H,A)
| ~ m0(J,H,A)
| p1(H,I,J) ),
inference(skolemisation,[status(esa)],[f119_nnf]) ).
cnf(c119,plain,
( ~ p1(X2,X0,X3)
| ~ m0(X2,X0,X3)
| p1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f119_sk]) ).
cnf(hi117,axiom,
ifeq(m0(X0,X1,X2),true,ifeq(p1(X0,X1,X2),true,p1(X1,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(f30,axiom,
m0(b,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
fof(f30_nnf,plain,
m0(b,b,e),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
m0(b,b,e),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(hi30,axiom,
m0(b,b,e) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(h168,plain,
p1(b,V0,b) = true,
inference(hyper_resolution,[status(thm)],[hi117,hi30,h28]) ).
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(h403,plain,
q2(b,a,b) = true,
inference(hyper_resolution,[status(thm)],[hi216,h168,h198,h188]) ).
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(h519,plain,
s2(a) = true,
inference(hyper_resolution,[status(thm)],[hi223,h403,h51]) ).
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(t5,plain,
s3(a,X1) = true,
inference(hyper_resolution,[status(thm)],[hi305,h403,h519,hi18]) ).
cnf(t37,plain,
s3(a,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f368,negated_conjecture,
~ s3(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ s3(a,d),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ s3(a,d),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ s3(a,d),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
s3(a,d) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t37]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN205-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n007.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 : Fri Sep 25 00:27:24 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.46/1.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.46/1.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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