%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN192-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 6.40s 1.32s
% Output : Proof 6.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 110 ( 62 unt; 0 def)
% Number of atoms : 206 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 198 ( 102 ~; 96 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 172 ( 49 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(h26,plain,
s1(b) = true,
inference(hyper_resolution,[status(thm)],[hi160,hi13]) ).
cnf(f170,axiom,
( ~ m0(C,B,J)
| ~ s1(B)
| ~ p0(A,A)
| l2(J,J) ),
file('/export/starexec/sandbox/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(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(h112,plain,
l2(e,e) = true,
inference(hyper_resolution,[status(thm)],[hi167,hi13,h26,hi30]) ).
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(f1,axiom,
q0(e,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f1_nnf,plain,
q0(e,d),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
q0(e,d),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi1,axiom,
q0(e,d) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h118,plain,
s1(e) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi1,h26]) ).
cnf(f143,axiom,
( ~ s0(B)
| q1(B,B,B) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/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(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/sandbox/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/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(h182,plain,
r2(a) = true,
inference(hyper_resolution,[status(thm)],[hi222,h122,hi19]) ).
cnf(f295,axiom,
( ~ l2(A,A)
| ~ s1(J)
| ~ r2(I)
| q3(I,I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_258) ).
fof(f295_nnf,plain,
! [I,J,A] :
( ~ l2(A,A)
| ~ s1(J)
| ~ r2(I)
| q3(I,I) ),
inference(nnf_transformation,[status(thm)],[f295]) ).
fof(f295_sk,plain,
! [I,J,A] :
( ~ l2(A,A)
| ~ s1(J)
| ~ r2(I)
| q3(I,I) ),
inference(skolemisation,[status(esa)],[f295_nnf]) ).
cnf(c295,plain,
( ~ l2(X2,X2)
| ~ s1(X1)
| ~ r2(X0)
| q3(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f295_sk]) ).
cnf(hi290,axiom,
ifeq(r2(X0),true,ifeq(s1(X1),true,ifeq(l2(X2,X2),true,q3(X0,X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c295]) ).
cnf(h252,plain,
q3(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi290,h182,h118,h112]) ).
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(h30,plain,
p1(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi120,hi13]) ).
cnf(f129,axiom,
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
file('/export/starexec/sandbox/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(f2,axiom,
n0(d,e),
file('/export/starexec/sandbox/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(h29,plain,
q1(V0,e,V0) = true,
inference(hyper_resolution,[status(thm)],[hi127,hi2,hi13]) ).
cnf(f206,axiom,
( ~ p1(D,F,D)
| ~ q1(E,E,E)
| p2(D,D,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_169) ).
fof(f206_nnf,plain,
! [D,E,F] :
( ~ p1(D,F,D)
| ~ q1(E,E,E)
| p2(D,D,D) ),
inference(nnf_transformation,[status(thm)],[f206]) ).
fof(f206_sk,plain,
! [D,E,F] :
( ~ p1(D,F,D)
| ~ q1(E,E,E)
| p2(D,D,D) ),
inference(skolemisation,[status(esa)],[f206_nnf]) ).
cnf(c206,plain,
( ~ p1(X0,X2,X0)
| ~ q1(X1,X1,X1)
| p2(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f206_sk]) ).
cnf(hi203,axiom,
ifeq(q1(X0,X0,X0),true,ifeq(p1(X1,X2,X1),true,p2(X1,X1,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c206]) ).
cnf(h173,plain,
p2(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi203,h29,h30]) ).
cnf(f277,axiom,
( ~ p2(E,F,D)
| n3(D) ),
file('/export/starexec/sandbox/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(h339,plain,
n3(V0) = true,
inference(hyper_resolution,[status(thm)],[hi272,h173]) ).
cnf(f335,axiom,
( ~ p0(J,G)
| ~ q3(H,I)
| ~ n3(G)
| r4(G) ),
file('/export/starexec/sandbox/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(t6,plain,
r4(X1) = true,
inference(hyper_resolution,[status(thm)],[hi328,h339,h252,hi13]) ).
cnf(t70,plain,
r4(X1) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(f368,negated_conjecture,
~ r4(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ r4(a),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ r4(a),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ r4(a),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
r4(a) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t70]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN192-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n010.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 00:27:44 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.40/1.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.40/1.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------