%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO612+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 : 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 01:18:17 PM UTC 2026
% Result : Theorem 10.85s 1.89s
% Output : Proof 10.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 105 ( 61 unt; 0 def)
% Number of atoms : 197 ( 55 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 140 ( 48 ~; 42 |; 38 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 244 ( 0 sgn 147 !; 9 ?)
% 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,O,G,D,E,F,NWPNT1] :
( ( coll(F,B,C)
& perp(F,D,B,C)
& coll(E,A,C)
& perp(E,D,A,C)
& coll(D,C,G)
& circle(O,C,D,NWPNT1)
& coll(G,A,B)
& perp(G,C,A,B)
& circle(O,A,B,C) )
=> cyclic(A,E,F,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618074) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,G,D,E,F,NWPNT1] :
( ( coll(F,B,C)
& perp(F,D,B,C)
& coll(E,A,C)
& perp(E,D,A,C)
& coll(D,C,G)
& circle(O,C,D,NWPNT1)
& coll(G,A,B)
& perp(G,C,A,B)
& circle(O,A,B,C) )
=> cyclic(A,E,F,B) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,G,D,E,F,NWPNT1] :
( ~ cyclic(A,E,F,B)
& coll(F,B,C)
& perp(F,D,B,C)
& coll(E,A,C)
& perp(E,D,A,C)
& coll(D,C,G)
& circle(O,C,D,NWPNT1)
& coll(G,A,B)
& perp(G,C,A,B)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cyclic(sk20,sk26,sk27,sk21)
& coll(sk27,sk21,sk22)
& perp(sk27,sk25,sk21,sk22)
& coll(sk26,sk20,sk22)
& perp(sk26,sk25,sk20,sk22)
& coll(sk25,sk22,sk24)
& circle(sk23,sk22,sk25,sk28)
& coll(sk24,sk20,sk21)
& perp(sk24,sk22,sk20,sk21)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28])],[f94_nnf]) ).
cnf(c115,plain,
coll(sk24,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
coll(sk24,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h0,plain,
coll(sk21,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi115,hi115]) ).
cnf(h12,plain,
coll(sk24,sk24,sk21) = 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(c114,plain,
perp(sk24,sk22,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
perp(sk24,sk22,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h339,plain,
perp(sk20,sk21,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi114]) ).
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(h345,plain,
para(sk24,sk22,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi114,h339]) ).
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(h491,plain,
eqangle(sk24,sk22,V0,V1,sk24,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h345]) ).
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(h2961,plain,
cyclic(sk22,sk21,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi42,h491,h12]) ).
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(h2980,plain,
cyclic(sk22,sk24,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2961]) ).
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(h3012,plain,
cyclic(sk22,sk24,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2980]) ).
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(sk20,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi115]) ).
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(h15,plain,
coll(sk20,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1]) ).
cnf(h45,plain,
coll(sk24,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h15,h15]) ).
cnf(h2959,plain,
cyclic(sk22,sk20,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi42,h491,h45]) ).
cnf(h2976,plain,
cyclic(sk22,sk24,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2959]) ).
cnf(h3003,plain,
cyclic(sk22,sk24,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2976]) ).
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(h3080,plain,
cyclic(sk24,sk24,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi16,h3003,h3012]) ).
cnf(h2,plain,
coll(sk24,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi115]) ).
cnf(h16,plain,
coll(sk20,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h2]) ).
cnf(c119,plain,
coll(sk26,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
coll(sk26,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h8,plain,
coll(sk26,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi119]) ).
cnf(h28,plain,
coll(sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h8,h8]) ).
cnf(h76,plain,
coll(sk26,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h28,h16]) ).
cnf(h149,plain,
coll(sk26,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h76]) ).
cnf(h274,plain,
coll(sk24,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h149,h149]) ).
cnf(h2957,plain,
cyclic(sk22,sk26,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi42,h491,h274]) ).
cnf(h2971,plain,
cyclic(sk22,sk24,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2957]) ).
cnf(h2995,plain,
cyclic(sk22,sk24,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2971]) ).
cnf(h3055,plain,
cyclic(sk24,sk24,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi16,h3003,h2995]) ).
cnf(h3807,plain,
cyclic(sk24,sk20,sk26,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi16,h3055,h3080]) ).
cnf(c121,plain,
coll(sk27,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi121,negated_conjecture,
coll(sk27,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(h11,plain,
coll(sk27,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi121]) ).
cnf(h36,plain,
coll(sk21,sk21,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,h11,h11]) ).
cnf(h96,plain,
coll(sk27,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h36,h0]) ).
cnf(h180,plain,
coll(sk27,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h96]) ).
cnf(h317,plain,
coll(sk24,sk24,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,h180,h180]) ).
cnf(h2956,plain,
cyclic(sk22,sk27,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi42,h491,h317]) ).
cnf(h2968,plain,
cyclic(sk22,sk24,sk27,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2956]) ).
cnf(h2989,plain,
cyclic(sk22,sk24,sk24,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2968]) ).
cnf(h3056,plain,
cyclic(sk24,sk24,sk20,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi16,h3003,h2989]) ).
cnf(h3184,plain,
cyclic(sk24,sk20,sk26,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi16,h3055,h3056]) ).
cnf(t34,plain,
cyclic(sk20,sk26,sk27,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi16,h3184,h3807]) ).
cnf(t3010,plain,
cyclic(sk20,sk26,sk27,sk21) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(c122,plain,
~ cyclic(sk20,sk26,sk27,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cyclic(sk20,sk26,sk27,sk21) != true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3010]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO612+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 12:33:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.85/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.85/1.89 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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