%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN218-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 03:34:06 PM UTC 2026
% Result : Unsatisfiable 6.93s 1.32s
% Output : Proof 6.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 46 unt; 0 def)
% Number of atoms : 82 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 71 ( 26 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f368,negated_conjecture,
~ l2(c,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
! [X] : ~ l2(c,X),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
! [X] : ~ l2(c,X),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ l2(c,X0),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(t68,plain,
eq(l2(c,X1),true) = efalse,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(t921,plain,
eq(l2(c,X1),true) = efalse,
inference(orient,[status(thm)],[t68]) ).
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(h8,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(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(h15,plain,
s1(e) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi1,h8]) ).
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(h16,plain,
s1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi16,h15]) ).
cnf(f24,axiom,
q0(d,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
fof(f24_nnf,plain,
q0(d,d),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
q0(d,d),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(hi24,axiom,
q0(d,d) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h25,plain,
s1(d) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi24,h16]) ).
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(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(t9,plain,
l2(X1,X1) = true,
inference(hyper_resolution,[status(thm)],[hi167,hi13,h25,hi18]) ).
cnf(t917,plain,
l2(X1,X1) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t922,plain,
efalse = eq(true,true),
inference(cp,[status(thm)],[t921,t917]) ).
cnf(t8,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t920,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t8]) ).
cnf(t979,plain,
efalse = etrue,
inference(step,[status(thm)],[t922,t920]) ).
cnf(t923,plain,
efalse = etrue,
inference(orient,[status(thm)],[t979]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t923]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN218-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n005.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 00:31:32 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.93/1.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.93/1.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------