%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN191-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 03:34:02 PM UTC 2026
% Result : Unsatisfiable 5.88s 1.40s
% Output : Proof 5.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 125 ( 73 unt; 0 def)
% Number of atoms : 225 ( 38 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 : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 186 ( 42 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f162,axiom,
( ~ p0(I,I)
| s1(I) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/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(h51,plain,
s1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi16,h34]) ).
cnf(f170,axiom,
( ~ m0(C,B,J)
| ~ s1(B)
| ~ p0(A,A)
| l2(J,J) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_133) ).
fof(f170_nnf,plain,
! [J,A,B,C] :
( ~ m0(C,B,J)
| ~ s1(B)
| ~ p0(A,A)
| l2(J,J) ),
inference(nnf_transformation,[status(thm)],[f170]) ).
fof(f170_sk,plain,
! [J,A,B,C] :
( ~ m0(C,B,J)
| ~ s1(B)
| ~ p0(A,A)
| l2(J,J) ),
inference(skolemisation,[status(esa)],[f170_nnf]) ).
cnf(c170,plain,
( ~ m0(X3,X2,X0)
| ~ s1(X2)
| ~ p0(X1,X1)
| l2(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f170_sk]) ).
cnf(hi167,axiom,
ifeq(p0(X0,X0),true,ifeq(s1(X1),true,ifeq(m0(X2,X1,X3),true,l2(X3,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c170]) ).
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(h115,plain,
l2(V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi167,hi13,h51,hi18]) ).
cnf(f302,axiom,
( ~ l2(G,F)
| r3(F,F,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_265) ).
fof(f302_nnf,plain,
! [F,G] :
( ~ l2(G,F)
| r3(F,F,F) ),
inference(nnf_transformation,[status(thm)],[f302]) ).
fof(f302_sk,plain,
! [F,G] :
( ~ l2(G,F)
| r3(F,F,F) ),
inference(skolemisation,[status(esa)],[f302_nnf]) ).
cnf(c302,plain,
( ~ l2(X1,X0)
| r3(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f302_sk]) ).
cnf(hi297,axiom,
ifeq(l2(X0,X1),true,r3(X1,X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c302]) ).
cnf(h128,plain,
r3(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi297,h115]) ).
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(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(h71,plain,
q1(V0,d,V0) = true,
inference(hyper_resolution,[status(thm)],[hi127,hi33,hi13]) ).
cnf(f161,axiom,
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_124) ).
fof(f161_nnf,plain,
! [D,E] :
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
inference(nnf_transformation,[status(thm)],[f161]) ).
fof(f161_sk,plain,
! [D,E] :
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
inference(skolemisation,[status(esa)],[f161_nnf]) ).
cnf(c161,plain,
( ~ q1(d,X1,d)
| ~ s0(d)
| ~ q0(X0,X1)
| r1(X0) ),
inference(cnf_transformation,[status(esa)],[f161_sk]) ).
cnf(hi159,axiom,
ifeq(q0(X0,X1),true,ifeq(s0(d),true,ifeq(q1(d,X1,d),true,r1(X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c161]) ).
cnf(f0,axiom,
s0(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f0_nnf,plain,
s0(d),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
s0(d),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,axiom,
s0(d) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h215,plain,
r1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi159,hi16,hi0,h71]) ).
cnf(f225,axiom,
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_188) ).
fof(f225_nnf,plain,
! [G] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(nnf_transformation,[status(thm)],[f225]) ).
fof(f225_sk,plain,
! [G] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(skolemisation,[status(esa)],[f225_nnf]) ).
cnf(c225,plain,
( ~ l0(X0)
| ~ r1(X0)
| r2(X0) ),
inference(cnf_transformation,[status(esa)],[f225_sk]) ).
cnf(hi222,axiom,
ifeq(r1(X0),true,ifeq(l0(X0),true,r2(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c225]) ).
cnf(f23,axiom,
l0(c),
file('/export/starexec/sandbox2/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(h216,plain,
r2(c) = true,
inference(hyper_resolution,[status(thm)],[hi222,h215,hi23]) ).
cnf(f132,axiom,
( ~ p0(G,F)
| q1(F,G,G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_095) ).
fof(f132_nnf,plain,
! [F,G] :
( ~ p0(G,F)
| q1(F,G,G) ),
inference(nnf_transformation,[status(thm)],[f132]) ).
fof(f132_sk,plain,
! [F,G] :
( ~ p0(G,F)
| q1(F,G,G) ),
inference(skolemisation,[status(esa)],[f132_nnf]) ).
cnf(c132,plain,
( ~ p0(X1,X0)
| q1(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f132_sk]) ).
cnf(hi130,axiom,
ifeq(p0(X0,X1),true,q1(X1,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c132]) ).
cnf(f17,axiom,
p0(c,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
fof(f17_nnf,plain,
p0(c,b),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
p0(c,b),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
p0(c,b) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h57,plain,
q1(b,c,c) = true,
inference(hyper_resolution,[status(thm)],[hi130,hi17]) ).
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(h207,plain,
k2(c,c) = true,
inference(hyper_resolution,[status(thm)],[hi164,h57]) ).
cnf(f38,axiom,
( ~ n0(J,I)
| k1(I) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_001) ).
fof(f38_nnf,plain,
! [I,J] :
( ~ n0(J,I)
| k1(I) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [I,J] :
( ~ n0(J,I)
| k1(I) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( ~ n0(X1,X0)
| k1(X0) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi38,axiom,
ifeq(n0(X0,X1),true,k1(X1),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(f25,axiom,
n0(d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
fof(f25_nnf,plain,
n0(d,c),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
n0(d,c),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(hi25,axiom,
n0(d,c) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h65,plain,
k1(c) = true,
inference(hyper_resolution,[status(thm)],[hi38,hi25]) ).
cnf(f66,axiom,
( ~ s0(H)
| ~ p0(H,I)
| m1(H,I,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_029) ).
fof(f66_nnf,plain,
! [H,I] :
( ~ s0(H)
| ~ p0(H,I)
| m1(H,I,H) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [H,I] :
( ~ s0(H)
| ~ p0(H,I)
| m1(H,I,H) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( ~ s0(X0)
| ~ p0(X0,X1)
| m1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(hi66,axiom,
ifeq(p0(X0,X1),true,ifeq(s0(X0),true,m1(X0,X1,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(f4,axiom,
s0(b),
file('/export/starexec/sandbox2/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(h49,plain,
m1(b,V0,b) = true,
inference(hyper_resolution,[status(thm)],[hi66,hi13,hi4]) ).
cnf(f164,axiom,
( ~ k2(F,D)
| ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_127) ).
fof(f164_nnf,plain,
! [C,D,E,F] :
( ~ k2(F,D)
| ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(nnf_transformation,[status(thm)],[f164]) ).
fof(f164_sk,plain,
! [C,D,E,F] :
( ~ k2(F,D)
| ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(skolemisation,[status(esa)],[f164_nnf]) ).
cnf(c164,plain,
( ~ k2(X3,X1)
| ~ k1(X3)
| ~ m1(X2,X1,X0)
| k2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f164_sk]) ).
cnf(hi162,axiom,
ifeq(m1(X0,X1,X2),true,ifeq(k1(X3),true,ifeq(k2(X3,X1),true,k2(X2,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c164]) ).
cnf(h209,plain,
k2(b,c) = true,
inference(hyper_resolution,[status(thm)],[hi162,h49,h65,h207]) ).
cnf(f309,axiom,
( ~ r3(B,J,J)
| ~ r2(B)
| ~ k2(A,B)
| r3(J,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_272) ).
fof(f309_nnf,plain,
! [J,A,B] :
( ~ r3(B,J,J)
| ~ r2(B)
| ~ k2(A,B)
| r3(J,A,B) ),
inference(nnf_transformation,[status(thm)],[f309]) ).
fof(f309_sk,plain,
! [J,A,B] :
( ~ r3(B,J,J)
| ~ r2(B)
| ~ k2(A,B)
| r3(J,A,B) ),
inference(skolemisation,[status(esa)],[f309_nnf]) ).
cnf(c309,plain,
( ~ r3(X2,X0,X0)
| ~ r2(X2)
| ~ k2(X1,X2)
| r3(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f309_sk]) ).
cnf(hi304,axiom,
ifeq(k2(X0,X1),true,ifeq(r2(X1),true,ifeq(r3(X1,X2,X2),true,r3(X2,X0,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c309]) ).
cnf(t32,plain,
r3(c,b,c) = true,
inference(hyper_resolution,[status(thm)],[hi304,h209,h216,h128]) ).
cnf(t59,plain,
r3(c,b,c) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(f368,negated_conjecture,
~ r3(c,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ r3(c,b,c),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ r3(c,b,c),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ r3(c,b,c),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
r3(c,b,c) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t59]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN191-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n017.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 00:22:16 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.88/1.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.88/1.40 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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