%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN144-1 : 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 03:33:55 PM UTC 2026
% Result : Unsatisfiable 7.91s 11.53s
% Output : Proof 7.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 105 ( 57 unt; 0 def)
% Number of atoms : 193 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 182 ( 94 ~; 88 |; 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 : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 136 ( 22 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f143,axiom,
( ~ s0(B)
| q1(B,B,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_106) ).
fof(f143_nnf,plain,
! [B] :
( ~ s0(B)
| q1(B,B,B) ),
inference(nnf_transformation,[status(thm)],[f143]) ).
fof(f143_sk,plain,
! [B] :
( ~ s0(B)
| q1(B,B,B) ),
inference(skolemisation,[status(esa)],[f143_nnf]) ).
cnf(c143,plain,
( ~ s0(X0)
| q1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f143_sk]) ).
cnf(hi141,axiom,
ifeq(s0(X0),true,q1(X0,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c143]) ).
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(h0,plain,
q1(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi141,hi0]) ).
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(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(h122,plain,
r1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi159,hi16,hi0,h0]) ).
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(f19,axiom,
l0(a),
file('/export/starexec/sandbox2/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(h182,plain,
r2(a) = true,
inference(hyper_resolution,[status(thm)],[hi222,h122,hi19]) ).
cnf(f303,axiom,
( ~ r2(E)
| r3(E,E,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_266) ).
fof(f303_nnf,plain,
! [E] :
( ~ r2(E)
| r3(E,E,E) ),
inference(nnf_transformation,[status(thm)],[f303]) ).
fof(f303_sk,plain,
! [E] :
( ~ r2(E)
| r3(E,E,E) ),
inference(skolemisation,[status(esa)],[f303_nnf]) ).
cnf(c303,plain,
( ~ r2(X0)
| r3(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f303_sk]) ).
cnf(hi298,axiom,
ifeq(r2(X0),true,r3(X0,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c303]) ).
cnf(h233,plain,
r3(a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi298,h182]) ).
cnf(f158,axiom,
( ~ m0(J,A,I)
| q1(I,I,I) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_121) ).
fof(f158_nnf,plain,
! [I,J,A] :
( ~ m0(J,A,I)
| q1(I,I,I) ),
inference(nnf_transformation,[status(thm)],[f158]) ).
fof(f158_sk,plain,
! [I,J,A] :
( ~ m0(J,A,I)
| q1(I,I,I) ),
inference(skolemisation,[status(esa)],[f158_nnf]) ).
cnf(c158,plain,
( ~ m0(X1,X2,X0)
| q1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f158_sk]) ).
cnf(hi156,axiom,
ifeq(m0(X0,X1,X2),true,q1(X2,X2,X2),true) = true,
inference(equality_encoding,[status(esa)],[c158]) ).
cnf(f3,axiom,
m0(e,d,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f3_nnf,plain,
m0(e,d,a),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
m0(e,d,a),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(hi3,axiom,
m0(e,d,a) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h7,plain,
q1(a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi156,hi3]) ).
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(h143,plain,
k2(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi164,h7]) ).
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(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(h110,plain,
k1(a) = true,
inference(hyper_resolution,[status(thm)],[hi38,hi36]) ).
cnf(f72,axiom,
( ~ l0(J)
| ~ r0(I)
| m1(I,J,I) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_035) ).
fof(f72_nnf,plain,
! [I,J] :
( ~ l0(J)
| ~ r0(I)
| m1(I,J,I) ),
inference(nnf_transformation,[status(thm)],[f72]) ).
fof(f72_sk,plain,
! [I,J] :
( ~ l0(J)
| ~ r0(I)
| m1(I,J,I) ),
inference(skolemisation,[status(esa)],[f72_nnf]) ).
cnf(c72,plain,
( ~ l0(X1)
| ~ r0(X0)
| m1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f72_sk]) ).
cnf(hi72,axiom,
ifeq(r0(X0),true,ifeq(l0(X1),true,m1(X0,X1,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(f12,axiom,
r0(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
fof(f12_nnf,plain,
r0(e),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
r0(e),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,axiom,
r0(e) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h41,plain,
m1(e,a,e) = true,
inference(hyper_resolution,[status(thm)],[hi72,hi12,hi19]) ).
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(h291,plain,
k2(e,a) = true,
inference(hyper_resolution,[status(thm)],[hi162,h41,h110,h143]) ).
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(h565,plain,
r3(a,e,a) = true,
inference(hyper_resolution,[status(thm)],[hi304,h291,h182,h233]) ).
cnf(f322,axiom,
( ~ r3(H,G,H)
| ~ r0(G)
| p4(G,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_285) ).
fof(f322_nnf,plain,
! [G,H] :
( ~ r3(H,G,H)
| ~ r0(G)
| p4(G,G,H) ),
inference(nnf_transformation,[status(thm)],[f322]) ).
fof(f322_sk,plain,
! [G,H] :
( ~ r3(H,G,H)
| ~ r0(G)
| p4(G,G,H) ),
inference(skolemisation,[status(esa)],[f322_nnf]) ).
cnf(c322,plain,
( ~ r3(X1,X0,X1)
| ~ r0(X0)
| p4(X0,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f322_sk]) ).
cnf(hi315,axiom,
ifeq(r0(X0),true,ifeq(r3(X1,X0,X1),true,p4(X0,X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c322]) ).
cnf(h775,plain,
p4(e,e,a) = true,
inference(hyper_resolution,[status(thm)],[hi315,hi12,h565]) ).
cnf(f340,axiom,
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_303) ).
fof(f340_nnf,plain,
! [D,E,F] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ),
inference(nnf_transformation,[status(thm)],[f340]) ).
fof(f340_sk,plain,
! [D,E,F] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ),
inference(skolemisation,[status(esa)],[f340_nnf]) ).
cnf(c340,plain,
( ~ p4(X0,X2,X1)
| ~ r0(X0)
| m5(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f340_sk]) ).
cnf(hi333,axiom,
ifeq(r0(X0),true,ifeq(p4(X0,X1,X2),true,m5(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c340]) ).
cnf(t57,plain,
m5(e,a) = true,
inference(hyper_resolution,[status(thm)],[hi333,hi12,h775]) ).
cnf(t160,plain,
m5(e,a) = true,
inference(orient,[status(thm)],[t57]) ).
cnf(f368,negated_conjecture,
~ m5(e,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ m5(e,a),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ m5(e,a),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ m5(e,a),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
m5(e,a) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t160]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN144-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.38 % Computer : n017.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Fri Sep 25 00:14:13 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.91/11.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.91/11.53 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------