%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN116-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 03:33:51 PM UTC 2026
% Result : Unsatisfiable 6.74s 1.31s
% Output : Proof 6.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 104 ( 60 unt; 0 def)
% Number of atoms : 188 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 174 ( 90 ~; 84 |; 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 : 145 ( 27 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f30,axiom,
m0(b,b,e),
file('/export/starexec/sandbox2/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(h9,plain,
m0(b,b,e) = true,
inference(hyper_resolution,[status(thm)],[hi30]) ).
cnf(f52,axiom,
( ~ m0(C,C,B)
| ~ l0(D)
| m1(B,C,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_015) ).
fof(f52_nnf,plain,
! [B,C,D] :
( ~ m0(C,C,B)
| ~ l0(D)
| m1(B,C,C) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [B,C,D] :
( ~ m0(C,C,B)
| ~ l0(D)
| m1(B,C,C) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c52,plain,
( ~ m0(X1,X1,X0)
| ~ l0(X2)
| m1(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi52,axiom,
ifeq(l0(X0),true,ifeq(m0(X1,X1,X2),true,m1(X2,X1,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
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(h10,plain,
m1(e,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi52,hi19,h9]) ).
cnf(f171,axiom,
( ~ p0(H,G)
| ~ m1(I,H,H)
| ~ m0(H,G,I)
| l2(G,G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_134) ).
fof(f171_nnf,plain,
! [G,H,I] :
( ~ p0(H,G)
| ~ m1(I,H,H)
| ~ m0(H,G,I)
| l2(G,G) ),
inference(nnf_transformation,[status(thm)],[f171]) ).
fof(f171_sk,plain,
! [G,H,I] :
( ~ p0(H,G)
| ~ m1(I,H,H)
| ~ m0(H,G,I)
| l2(G,G) ),
inference(skolemisation,[status(esa)],[f171_nnf]) ).
cnf(c171,plain,
( ~ p0(X1,X0)
| ~ m1(X2,X1,X1)
| ~ m0(X1,X0,X2)
| l2(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f171_sk]) ).
cnf(hi168,axiom,
ifeq(m0(X0,X1,X2),true,ifeq(m1(X2,X0,X0),true,ifeq(p0(X0,X1),true,l2(X1,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c171]) ).
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(h29,plain,
l2(b,b) = true,
inference(hyper_resolution,[status(thm)],[hi168,hi30,h10,hi13]) ).
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(h30,plain,
r3(b,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi297,h29]) ).
cnf(h11,plain,
l2(b,b) = true,
inference(hyper_resolution,[status(thm)],[hi168,hi30,h10,hi13]) ).
cnf(f31,axiom,
k0(b),
file('/export/starexec/sandbox2/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(h2,plain,
k0(b) = true,
inference(hyper_resolution,[status(thm)],[hi31]) ).
cnf(f6,axiom,
n0(d,b),
file('/export/starexec/sandbox2/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(h1,plain,
n0(d,b) = true,
inference(hyper_resolution,[status(thm)],[hi6]) ).
cnf(f100,axiom,
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
file('/export/starexec/sandbox2/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(h28,plain,
p1(b,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi99,h1,h2]) ).
cnf(f299,axiom,
( ~ r3(A,B,A)
| ~ l2(C,B)
| ~ p1(B,C,A)
| r3(A,A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_262) ).
fof(f299_nnf,plain,
! [A,B,C] :
( ~ r3(A,B,A)
| ~ l2(C,B)
| ~ p1(B,C,A)
| r3(A,A,A) ),
inference(nnf_transformation,[status(thm)],[f299]) ).
fof(f299_sk,plain,
! [A,B,C] :
( ~ r3(A,B,A)
| ~ l2(C,B)
| ~ p1(B,C,A)
| r3(A,A,A) ),
inference(skolemisation,[status(esa)],[f299_nnf]) ).
cnf(c299,plain,
( ~ r3(X0,X1,X0)
| ~ l2(X2,X1)
| ~ p1(X1,X2,X0)
| r3(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f299_sk]) ).
cnf(hi294,axiom,
ifeq(p1(X0,X1,X2),true,ifeq(l2(X1,X0),true,ifeq(r3(X2,X0,X2),true,r3(X2,X2,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c299]) ).
cnf(h31,plain,
r3(b,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi294,h28,h11,h30]) ).
cnf(f39,axiom,
( ~ n0(H,G)
| l1(G,G) ),
file('/export/starexec/sandbox2/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(f2,axiom,
n0(d,e),
file('/export/starexec/sandbox2/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(h26,plain,
l1(e,e) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi2]) ).
cnf(h3,plain,
p0(b,b) = true,
inference(hyper_resolution,[status(thm)],[hi13]) ).
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(h8,plain,
s1(b) = true,
inference(hyper_resolution,[status(thm)],[hi160,h3]) ).
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(h24,plain,
l2(e,e) = true,
inference(hyper_resolution,[status(thm)],[hi167,hi13,h8,hi30]) ).
cnf(f283,axiom,
( ~ l2(D,D)
| p3(D,D,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_246) ).
fof(f283_nnf,plain,
! [D] :
( ~ l2(D,D)
| p3(D,D,D) ),
inference(nnf_transformation,[status(thm)],[f283]) ).
fof(f283_sk,plain,
! [D] :
( ~ l2(D,D)
| p3(D,D,D) ),
inference(skolemisation,[status(esa)],[f283_nnf]) ).
cnf(c283,plain,
( ~ l2(X0,X0)
| p3(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f283_sk]) ).
cnf(hi278,axiom,
ifeq(l2(X0,X0),true,p3(X0,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c283]) ).
cnf(h25,plain,
p3(e,e,e) = true,
inference(hyper_resolution,[status(thm)],[hi278,h24]) ).
cnf(f336,axiom,
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_299) ).
fof(f336_nnf,plain,
! [A,B,C,D] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(nnf_transformation,[status(thm)],[f336]) ).
fof(f336_sk,plain,
! [A,B,C,D] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(skolemisation,[status(esa)],[f336_nnf]) ).
cnf(c336,plain,
( ~ l1(X0,X2)
| ~ p3(X1,X2,X3)
| s4(X0) ),
inference(cnf_transformation,[status(esa)],[f336_sk]) ).
cnf(hi329,axiom,
ifeq(p3(X0,X1,X2),true,ifeq(l1(X3,X1),true,s4(X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c336]) ).
cnf(h27,plain,
s4(e) = true,
inference(hyper_resolution,[status(thm)],[hi329,h25,h26]) ).
cnf(f337,axiom,
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_300) ).
fof(f337_nnf,plain,
! [E,F,G] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ),
inference(nnf_transformation,[status(thm)],[f337]) ).
fof(f337_sk,plain,
! [E,F,G] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ),
inference(skolemisation,[status(esa)],[f337_nnf]) ).
cnf(c337,plain,
( ~ r3(X2,X0,X0)
| ~ s4(X1)
| k5(X0) ),
inference(cnf_transformation,[status(esa)],[f337_sk]) ).
cnf(hi330,axiom,
ifeq(s4(X0),true,ifeq(r3(X1,X2,X2),true,k5(X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c337]) ).
cnf(t0,plain,
k5(b) = true,
inference(hyper_resolution,[status(thm)],[hi330,h27,h31]) ).
cnf(t1,plain,
k5(b) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f368,negated_conjecture,
~ k5(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ k5(b),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ k5(b),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ k5(b),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
k5(b) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN116-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 00:13:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.74/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.74/1.31 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------