%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO567+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 01:18:10 PM UTC 2026
% Result : Theorem 13.04s 7.08s
% Output : Proof 13.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 103 ( 59 unt; 0 def)
% Number of atoms : 183 ( 53 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 128 ( 48 ~; 42 |; 26 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 235 ( 0 sgn 141 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/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,Q,P] :
( ( coll(P,A,C)
& perp(P,D,A,C)
& coll(Q,A,B)
& perp(Q,D,A,B)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(B,Q,P,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL214029) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,Q,P] :
( ( coll(P,A,C)
& perp(P,D,A,C)
& coll(Q,A,B)
& perp(Q,D,A,B)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(B,Q,P,C) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,Q,P] :
( ~ cyclic(B,Q,P,C)
& coll(P,A,C)
& perp(P,D,A,C)
& coll(Q,A,B)
& perp(Q,D,A,B)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cyclic(sk21,sk24,sk25,sk22)
& coll(sk25,sk20,sk22)
& perp(sk25,sk23,sk20,sk22)
& coll(sk24,sk20,sk21)
& perp(sk24,sk23,sk20,sk21)
& coll(sk23,sk21,sk22)
& perp(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25])],[f94_nnf]) ).
cnf(c114,plain,
coll(sk23,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
coll(sk23,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h0,plain,
coll(sk22,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi114,hi114]) ).
cnf(h9,plain,
coll(sk23,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0,h0]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(c113,plain,
perp(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
perp(sk23,sk20,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h213,plain,
perp(sk21,sk22,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi113]) ).
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h219,plain,
para(sk23,sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi113,h213]) ).
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/sandbox2/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(h336,plain,
eqangle(sk23,sk20,V0,V1,sk23,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h219]) ).
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/sandbox2/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(h2178,plain,
cyclic(sk20,sk22,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h336,h9]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/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(h2196,plain,
cyclic(sk20,sk23,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2178]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/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(h2223,plain,
cyclic(sk20,sk23,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2196]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/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(h1,plain,
coll(sk21,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi114]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/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(h12,plain,
coll(sk21,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1]) ).
cnf(h36,plain,
coll(sk23,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h12,h12]) ).
cnf(h2177,plain,
cyclic(sk20,sk21,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h336,h36]) ).
cnf(h2193,plain,
cyclic(sk20,sk23,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2177]) ).
cnf(h2217,plain,
cyclic(sk20,sk23,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2193]) ).
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/sandbox2/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(h2284,plain,
cyclic(sk23,sk23,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi16,h2217,h2223]) ).
cnf(h2,plain,
coll(sk23,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi114]) ).
cnf(h13,plain,
coll(sk21,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h2]) ).
cnf(c116,plain,
coll(sk24,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk24,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h3,plain,
coll(sk21,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi116,hi116]) ).
cnf(h38,plain,
coll(sk24,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h3,h13]) ).
cnf(h80,plain,
coll(sk24,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h38]) ).
cnf(h139,plain,
coll(sk23,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h80,h80]) ).
cnf(h2174,plain,
cyclic(sk20,sk24,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h336,h139]) ).
cnf(h2185,plain,
cyclic(sk20,sk23,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2174]) ).
cnf(h2204,plain,
cyclic(sk20,sk23,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2185]) ).
cnf(h2273,plain,
cyclic(sk23,sk23,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi16,h2217,h2204]) ).
cnf(h3770,plain,
cyclic(sk23,sk21,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi16,h2273,h2284]) ).
cnf(c118,plain,
coll(sk25,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
coll(sk25,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h6,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi118,hi118]) ).
cnf(h23,plain,
coll(sk25,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h6,h0]) ).
cnf(h55,plain,
coll(sk25,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h23]) ).
cnf(h107,plain,
coll(sk23,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h55,h55]) ).
cnf(h2175,plain,
cyclic(sk20,sk25,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h336,h107]) ).
cnf(h2188,plain,
cyclic(sk20,sk23,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2175]) ).
cnf(h2209,plain,
cyclic(sk20,sk23,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2188]) ).
cnf(h2272,plain,
cyclic(sk23,sk23,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi16,h2217,h2209]) ).
cnf(h3738,plain,
cyclic(sk23,sk21,sk24,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi16,h2273,h2272]) ).
cnf(t35,plain,
cyclic(sk21,sk24,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi16,h3738,h3770]) ).
cnf(t3089,plain,
cyclic(sk21,sk24,sk25,sk22) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(c119,plain,
~ cyclic(sk21,sk24,sk25,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cyclic(sk21,sk24,sk25,sk22) != true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3089]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO567+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n004.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 12:25:13 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.04/7.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.04/7.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------