%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN137-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 03:33:54 PM UTC 2026
% Result : Unsatisfiable 6.81s 1.31s
% Output : Proof 6.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 86 ( 58 unt; 0 def)
% Number of atoms : 154 ( 29 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 142 ( 74 ~; 68 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 100 ( 21 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(h1,plain,
s0(d) = true,
inference(hyper_resolution,[status(thm)],[hi0]) ).
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(h12,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(h13,plain,
s1(a) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi16,h12]) ).
cnf(f227,axiom,
( ~ s0(d)
| ~ s1(a)
| s2(d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_190) ).
fof(f227_nnf,plain,
( ~ s0(d)
| ~ s1(a)
| s2(d) ),
inference(nnf_transformation,[status(thm)],[f227]) ).
fof(f227_sk,plain,
( ~ s0(d)
| ~ s1(a)
| s2(d) ),
inference(skolemisation,[status(esa)],[f227_nnf]) ).
cnf(c227,plain,
( ~ s0(d)
| ~ s1(a)
| s2(d) ),
inference(cnf_transformation,[status(esa)],[f227_sk]) ).
cnf(hi224,axiom,
ifeq(s1(a),true,ifeq(s0(d),true,s2(d),true),true) = true,
inference(equality_encoding,[status(esa)],[c227]) ).
cnf(h14,plain,
s2(d) = true,
inference(hyper_resolution,[status(thm)],[hi224,h13,h1]) ).
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(h4,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(h5,plain,
m1(e,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi52,hi19,h4]) ).
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(h6,plain,
l2(b,b) = true,
inference(hyper_resolution,[status(thm)],[hi168,hi30,h5,hi13]) ).
cnf(f10,axiom,
n0(e,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
fof(f10_nnf,plain,
n0(e,b),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
n0(e,b),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,axiom,
n0(e,b) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h0,plain,
n0(e,b) = true,
inference(hyper_resolution,[status(thm)],[hi10]) ).
cnf(h15,plain,
s1(b) = true,
inference(hyper_resolution,[status(thm)],[hi160,hi13]) ).
cnf(h16,plain,
s1(d) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi16,h15]) ).
cnf(f168,axiom,
( ~ l2(E,E)
| ~ n0(e,E)
| ~ s1(D)
| l2(D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_131) ).
fof(f168_nnf,plain,
! [D,E] :
( ~ l2(E,E)
| ~ n0(e,E)
| ~ s1(D)
| l2(D,E) ),
inference(nnf_transformation,[status(thm)],[f168]) ).
fof(f168_sk,plain,
! [D,E] :
( ~ l2(E,E)
| ~ n0(e,E)
| ~ s1(D)
| l2(D,E) ),
inference(skolemisation,[status(esa)],[f168_nnf]) ).
cnf(c168,plain,
( ~ l2(X1,X1)
| ~ n0(e,X1)
| ~ s1(X0)
| l2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f168_sk]) ).
cnf(hi166,axiom,
ifeq(s1(X0),true,ifeq(n0(e,X1),true,ifeq(l2(X1,X1),true,l2(X0,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c168]) ).
cnf(h17,plain,
l2(d,b) = true,
inference(hyper_resolution,[status(thm)],[hi166,h16,h0,h6]) ).
cnf(f262,axiom,
( ~ s2(B)
| ~ m0(J,C,C)
| ~ l2(C,J)
| ~ m0(B,B,A)
| m3(J,A,J) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_225) ).
fof(f262_nnf,plain,
! [J,A,B,C] :
( ~ s2(B)
| ~ m0(J,C,C)
| ~ l2(C,J)
| ~ m0(B,B,A)
| m3(J,A,J) ),
inference(nnf_transformation,[status(thm)],[f262]) ).
fof(f262_sk,plain,
! [J,A,B,C] :
( ~ s2(B)
| ~ m0(J,C,C)
| ~ l2(C,J)
| ~ m0(B,B,A)
| m3(J,A,J) ),
inference(skolemisation,[status(esa)],[f262_nnf]) ).
cnf(c262,plain,
( ~ s2(X2)
| ~ m0(X0,X3,X3)
| ~ l2(X3,X0)
| ~ m0(X2,X2,X1)
| m3(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f262_sk]) ).
cnf(hi257,axiom,
ifeq(m0(X0,X0,X1),true,ifeq(l2(X2,X3),true,ifeq(m0(X3,X2,X2),true,ifeq(s2(X0),true,m3(X3,X1,X3),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c262]) ).
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(t0,plain,
m3(b,c,b) = true,
inference(hyper_resolution,[status(thm)],[hi257,hi18,h17,hi18,h14]) ).
cnf(t13,plain,
m3(b,c,b) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f368,negated_conjecture,
~ m3(b,c,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ m3(b,c,b),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ m3(b,c,b),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ m3(b,c,b),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
m3(b,c,b) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN137-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n009.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 00:16:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.81/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.81/1.31 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------