%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO657+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 01:18:24 PM UTC 2026
% Result : Theorem 56.22s 7.70s
% Output : Proof 56.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 18
% Syntax : Number of formulae : 162 ( 90 unt; 0 def)
% Number of atoms : 302 ( 83 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 236 ( 96 ~; 90 |; 31 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 398 ( 0 sgn 239 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G] :
( ( coll(G,B,C)
& coll(F,C,D)
& para(A,D,F,E)
& para(A,B,G,E)
& coll(E,A,C) )
=> para(B,D,G,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULLmoreE02315) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( coll(G,B,C)
& coll(F,C,D)
& para(A,D,F,E)
& para(A,B,G,E)
& coll(E,A,C) )
=> para(B,D,G,F) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G] :
( ~ para(B,D,G,F)
& coll(G,B,C)
& coll(F,C,D)
& para(A,D,F,E)
& para(A,B,G,E)
& coll(E,A,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk21,sk23,sk26,sk25)
& coll(sk26,sk21,sk22)
& coll(sk25,sk22,sk23)
& para(sk20,sk23,sk25,sk24)
& para(sk20,sk21,sk26,sk24)
& coll(sk24,sk20,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26])],[f94_nnf]) ).
cnf(c117,plain,
coll(sk26,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk26,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h6,plain,
coll(sk22,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi117,hi117]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c116,plain,
coll(sk25,sk22,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk25,sk22,sk23) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h5,plain,
coll(sk25,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi116]) ).
cnf(h19,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h5,h5]) ).
cnf(h51,plain,
coll(sk25,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h19,h6]) ).
cnf(h100,plain,
coll(sk25,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h51]) ).
cnf(h187,plain,
coll(sk23,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi116,h100]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(c115,plain,
para(sk20,sk23,sk25,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
para(sk20,sk23,sk25,sk24) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h343,plain,
para(sk20,sk23,sk24,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi115]) ).
cnf(c113,plain,
coll(sk24,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
coll(sk24,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
coll(sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi113,hi113]) ).
cnf(h22,plain,
coll(sk24,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0,h6]) ).
cnf(h56,plain,
coll(sk24,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h22]) ).
cnf(h2,plain,
coll(sk24,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi113]) ).
cnf(h109,plain,
coll(sk20,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h56]) ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD5) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c114,plain,
para(sk20,sk21,sk26,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
para(sk20,sk21,sk26,sk24) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h340,plain,
para(sk26,sk24,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi114]) ).
cnf(h346,plain,
para(sk26,sk24,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi3,h340]) ).
cnf(h355,plain,
para(sk21,sk20,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi4,h346]) ).
cnf(h341,plain,
para(sk20,sk21,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi114]) ).
cnf(h348,plain,
para(sk24,sk26,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi4,h341]) ).
fof(f5,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD6) ).
fof(f5_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(para(X0,X1,X2,X3),true,ifeq(para(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h357,plain,
para(sk24,sk26,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi5,h348,h341]) ).
cnf(h342,plain,
para(sk25,sk24,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi115]) ).
cnf(h350,plain,
para(sk25,sk24,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi5,h342,hi115]) ).
cnf(h3,plain,
coll(sk23,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi116,hi116]) ).
cnf(h15,plain,
coll(sk25,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h3,h3]) ).
cnf(h40,plain,
coll(sk25,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h15]) ).
cnf(h84,plain,
coll(sk25,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h40,h5]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h7,plain,
coll(sk21,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi117]) ).
cnf(h25,plain,
coll(sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h7,h7]) ).
cnf(h60,plain,
coll(sk25,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h19,h25]) ).
cnf(h119,plain,
coll(sk25,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h60]) ).
cnf(h212,plain,
coll(sk21,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h119,h84]) ).
cnf(h344,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi114,h340]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h1111,plain,
eqangle(sk20,sk21,V0,V1,sk20,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h344]) ).
cnf(h1,plain,
coll(sk20,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi113]) ).
cnf(h11,plain,
coll(sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1,h1]) ).
cnf(h50,plain,
coll(sk25,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h19,h11]) ).
cnf(h99,plain,
coll(sk25,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h50]) ).
cnf(h179,plain,
coll(sk20,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h99,h99]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(h3918,plain,
cyclic(sk21,sk25,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h1111,h179]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD15) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h3932,plain,
cyclic(sk21,sk20,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h3918]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X1,X0,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h3956,plain,
cyclic(sk20,sk21,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi15,h3932]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD14) ).
fof(f13_nnf,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h4004,plain,
cyclic(sk20,sk21,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi13,h3956]) ).
fof(f16,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD17) ).
fof(f16_nnf,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,cyclic(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h4366,plain,
cyclic(sk21,sk20,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi16,h4004,h4004]) ).
cnf(h6106,plain,
cyclic(sk21,sk25,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi14,h4366]) ).
cnf(h64,plain,
coll(sk21,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h25,h11]) ).
cnf(h123,plain,
coll(sk21,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h64]) ).
cnf(h241,plain,
coll(sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h123,h123]) ).
cnf(h3917,plain,
cyclic(sk21,sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h1111,h241]) ).
cnf(h3929,plain,
cyclic(sk21,sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h3917]) ).
cnf(h3950,plain,
cyclic(sk20,sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi15,h3929]) ).
cnf(h3990,plain,
cyclic(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi13,h3950]) ).
cnf(h4369,plain,
cyclic(sk21,sk20,sk25,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi16,h4004,h3990]) ).
cnf(h6112,plain,
cyclic(sk21,sk25,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi14,h4369]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi43,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,ifeq(cyclic(X0,X1,X2,X5),true,ifeq(eqangle(X2,X0,X2,X1,X5,X3,X5,X4),true,cong(X0,X1,X3,X4),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(h11395,plain,
cong(sk21,sk25,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi43,h6112,h6106,h3918,h1111]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(hi67,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(coll(X0,X1,X2),true,midp(X0,X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(h24660,plain,
midp(sk21,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi67,h11395,h212]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(hi64,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(para(X1,X3,X2,X4),true,ifeq(para(X1,X4,X2,X3),true,midp(X0,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(h24945,plain,
midp(sk21,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi64,h24660,h350,h350]) ).
cnf(h25242,plain,
midp(sk21,sk26,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi64,h24945,h357,h357]) ).
fof(f45,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD45) ).
fof(f45_nnf,plain,
! [A,B,C,E,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [E,A,B,F,C] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
( midp(X4,X0,X2)
| ~ coll(X4,X0,X2)
| ~ para(X3,X4,X1,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(hi45,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(para(X0,X3,X2,X4),true,ifeq(coll(X3,X1,X4),true,midp(X3,X1,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(h25569,plain,
midp(sk20,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi45,h25242,h355,h109]) ).
cnf(h26244,plain,
midp(sk23,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi45,h25569,h343,h187]) ).
fof(f44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD44) ).
fof(f44_nnf,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [E,A,B,F,C] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( para(X3,X4,X1,X2)
| ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi44,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X3,X1,X4),true,para(X0,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(t35,plain,
para(sk21,sk23,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi44,h25242,h26244]) ).
cnf(t2134,plain,
para(sk21,sk23,sk26,sk25) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(c118,plain,
~ para(sk21,sk23,sk26,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk21,sk23,sk26,sk25) != true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2134]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO657+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n003.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 : Wed Sep 23 12:42:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 56.22/7.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 56.22/7.70 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------