%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN202-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 03:34:03 PM UTC 2026
% Result : Unsatisfiable 6.21s 1.19s
% Output : Proof 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 87 ( 55 unt; 0 def)
% Number of atoms : 147 ( 26 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 126 ( 66 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 97 ( 28 sgn 38 !; 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(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(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(h117,plain,
s1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi16,h26]) ).
cnf(f103,axiom,
( ~ n0(H,G)
| p1(G,G,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_066) ).
fof(f103_nnf,plain,
! [G,H] :
( ~ n0(H,G)
| p1(G,G,G) ),
inference(nnf_transformation,[status(thm)],[f103]) ).
fof(f103_sk,plain,
! [G,H] :
( ~ n0(H,G)
| p1(G,G,G) ),
inference(skolemisation,[status(esa)],[f103_nnf]) ).
cnf(c103,plain,
( ~ n0(X1,X0)
| p1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f103_sk]) ).
cnf(hi102,axiom,
ifeq(n0(X0,X1),true,p1(X1,X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c103]) ).
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(h4,plain,
p1(e,e,e) = true,
inference(hyper_resolution,[status(thm)],[hi102,hi2]) ).
cnf(f218,axiom,
( ~ p1(I,I,I)
| q2(I,I,I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_181) ).
fof(f218_nnf,plain,
! [I] :
( ~ p1(I,I,I)
| q2(I,I,I) ),
inference(nnf_transformation,[status(thm)],[f218]) ).
fof(f218_sk,plain,
! [I] :
( ~ p1(I,I,I)
| q2(I,I,I) ),
inference(skolemisation,[status(esa)],[f218_nnf]) ).
cnf(c218,plain,
( ~ p1(X0,X0,X0)
| q2(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f218_sk]) ).
cnf(hi215,axiom,
ifeq(p1(X0,X0,X0),true,q2(X0,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c218]) ).
cnf(h135,plain,
q2(e,e,e) = true,
inference(hyper_resolution,[status(thm)],[hi215,h4]) ).
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(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(h123,plain,
r1(e) = true,
inference(hyper_resolution,[status(thm)],[hi159,hi1,hi0,h0]) ).
cnf(f224,axiom,
( ~ q2(D,D,D)
| ~ k0(D)
| ~ m0(E,F,C)
| ~ r1(D)
| q2(C,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_187) ).
fof(f224_nnf,plain,
! [C,D,E,F] :
( ~ q2(D,D,D)
| ~ k0(D)
| ~ m0(E,F,C)
| ~ r1(D)
| q2(C,D,C) ),
inference(nnf_transformation,[status(thm)],[f224]) ).
fof(f224_sk,plain,
! [C,D,E,F] :
( ~ q2(D,D,D)
| ~ k0(D)
| ~ m0(E,F,C)
| ~ r1(D)
| q2(C,D,C) ),
inference(skolemisation,[status(esa)],[f224_nnf]) ).
cnf(c224,plain,
( ~ q2(X1,X1,X1)
| ~ k0(X1)
| ~ m0(X2,X3,X0)
| ~ r1(X1)
| q2(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f224_sk]) ).
cnf(hi221,axiom,
ifeq(r1(X0),true,ifeq(m0(X1,X2,X3),true,ifeq(k0(X0),true,ifeq(q2(X0,X0,X0),true,q2(X3,X0,X3),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c224]) ).
cnf(f18,axiom,
m0(X,d,Y),
file('/export/starexec/sandbox/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(f27,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
fof(f27_nnf,plain,
k0(e),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
k0(e),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi27,axiom,
k0(e) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h294,plain,
q2(V0,e,V0) = true,
inference(hyper_resolution,[status(thm)],[hi221,h123,hi18,hi27,h135]) ).
cnf(f226,axiom,
( ~ s1(b)
| ~ q2(b,H,b)
| s2(H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_189) ).
fof(f226_nnf,plain,
! [H] :
( ~ s1(b)
| ~ q2(b,H,b)
| s2(H) ),
inference(nnf_transformation,[status(thm)],[f226]) ).
fof(f226_sk,plain,
! [H] :
( ~ s1(b)
| ~ q2(b,H,b)
| s2(H) ),
inference(skolemisation,[status(esa)],[f226_nnf]) ).
cnf(c226,plain,
( ~ s1(b)
| ~ q2(b,X0,b)
| s2(X0) ),
inference(cnf_transformation,[status(esa)],[f226_sk]) ).
cnf(hi223,axiom,
ifeq(q2(b,X0,b),true,ifeq(s1(b),true,s2(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c226]) ).
cnf(t25,plain,
s2(e) = true,
inference(hyper_resolution,[status(thm)],[hi223,h294,h117]) ).
cnf(t612,plain,
s2(e) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(f368,negated_conjecture,
~ s2(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ s2(e),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ s2(e),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ s2(e),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
s2(e) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t612]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN202-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 00:28:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.21/1.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.21/1.19 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------