%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO578+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 : n006.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 01:18:12 PM UTC 2026
% Result : Theorem 10.61s 1.78s
% Output : Proof 10.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 22
% Syntax : Number of formulae : 195 ( 107 unt; 0 def)
% Number of atoms : 355 ( 103 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 271 ( 111 ~; 105 |; 32 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 467 ( 0 sgn 280 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
fof(f94,conjecture,
! [A,B,C,I,E] :
( ( coll(E,A,C)
& para(A,B,E,I)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) )
=> cong(E,I,E,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL214040) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,I,E] :
( ( coll(E,A,C)
& para(A,B,E,I)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) )
=> cong(E,I,E,A) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,I,E] :
( ~ cong(E,I,E,A)
& coll(E,A,C)
& para(A,B,E,I)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cong(sk24,sk23,sk24,sk20)
& coll(sk24,sk20,sk22)
& para(sk20,sk21,sk24,sk23)
& eqangle(sk23,sk22,sk22,sk20,sk23,sk22,sk22,sk21)
& eqangle(sk23,sk21,sk21,sk22,sk23,sk21,sk21,sk20)
& eqangle(sk23,sk20,sk20,sk21,sk23,sk20,sk20,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24])],[f94_nnf]) ).
cnf(c116,plain,
para(sk20,sk21,sk24,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
para(sk20,sk21,sk24,sk23) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h27,plain,
para(sk24,sk23,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi116]) ).
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(h31,plain,
para(sk24,sk23,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi5,h27,hi116]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h111,plain,
coll(sk24,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi66,h31]) ).
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]) ).
cnf(h114,plain,
coll(sk23,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h111,h111]) ).
cnf(h116,plain,
coll(sk24,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h114,h114]) ).
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(c117,plain,
coll(sk24,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk24,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h1,plain,
coll(sk20,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,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(h6,plain,
coll(sk20,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1]) ).
cnf(h14,plain,
coll(sk24,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h6,h6]) ).
cnf(h124,plain,
coll(sk20,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h14,h116]) ).
cnf(h131,plain,
coll(sk20,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h124]) ).
cnf(h0,plain,
coll(sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi117,hi117]) ).
cnf(h3,plain,
coll(sk24,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0,h0]) ).
cnf(h9,plain,
coll(sk24,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3]) ).
cnf(h2,plain,
coll(sk24,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi117]) ).
cnf(h19,plain,
coll(sk20,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h9]) ).
cnf(h160,plain,
coll(sk24,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h19,h131]) ).
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(h28,plain,
para(sk20,sk21,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi116]) ).
cnf(h35,plain,
para(sk23,sk24,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi4,h28]) ).
cnf(h583,plain,
para(sk23,sk24,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi3,h35]) ).
cnf(h7,plain,
coll(sk20,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h2]) ).
cnf(h30,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi116,h27]) ).
cnf(h36,plain,
coll(sk20,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi66,h30]) ).
cnf(h40,plain,
coll(sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h36,h36]) ).
cnf(h42,plain,
coll(sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h40,h40]) ).
cnf(h53,plain,
coll(sk21,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h42,h7]) ).
cnf(h62,plain,
coll(sk21,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h53]) ).
cnf(h88,plain,
coll(sk24,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h62,h62]) ).
cnf(h126,plain,
coll(sk23,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h116,h88]) ).
cnf(h133,plain,
coll(sk23,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h126]) ).
cnf(h115,plain,
coll(sk23,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi1,h111]) ).
cnf(h181,plain,
coll(sk23,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h115,h133]) ).
cnf(h182,plain,
coll(sk21,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h133,h115]) ).
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(h37,plain,
eqangle(sk20,sk21,V0,V1,sk20,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h30]) ).
cnf(h128,plain,
coll(sk23,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h116,h14]) ).
cnf(h139,plain,
coll(sk23,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h128]) ).
cnf(h183,plain,
coll(sk20,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h139,h139]) ).
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(h1055,plain,
cyclic(sk21,sk23,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h37,h183]) ).
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(h1065,plain,
cyclic(sk21,sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h1055]) ).
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(h1079,plain,
cyclic(sk20,sk21,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi15,h1065]) ).
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(h1104,plain,
cyclic(sk20,sk21,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi13,h1079]) ).
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(h1154,plain,
cyclic(sk21,sk20,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi16,h1104,h1104]) ).
cnf(h1384,plain,
cyclic(sk21,sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi14,h1154]) ).
cnf(h1056,plain,
cyclic(sk21,sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h37,h42]) ).
cnf(h1066,plain,
cyclic(sk21,sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h1056]) ).
cnf(h1082,plain,
cyclic(sk20,sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi15,h1066]) ).
cnf(h1110,plain,
cyclic(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi13,h1082]) ).
cnf(h1162,plain,
cyclic(sk21,sk20,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi16,h1104,h1110]) ).
cnf(h1400,plain,
cyclic(sk21,sk23,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi14,h1162]) ).
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(h2288,plain,
cong(sk21,sk23,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi43,h1400,h1384,h1055,h37]) ).
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(h3411,plain,
midp(sk21,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi67,h2288,h182]) ).
cnf(h38,plain,
para(sk20,sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi3,h30]) ).
cnf(h16,plain,
coll(sk20,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7]) ).
cnf(h23,plain,
coll(sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h16,h16]) ).
cnf(h48,plain,
coll(sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h23,h42]) ).
cnf(h32,plain,
para(sk24,sk23,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi3,h27]) ).
cnf(h468,plain,
para(sk21,sk20,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi4,h32]) ).
cnf(h698,plain,
para(sk21,sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi5,h468,h32]) ).
cnf(h51,plain,
coll(sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h42,h23]) ).
cnf(h1057,plain,
cyclic(sk21,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h37,h23]) ).
cnf(h1083,plain,
cyclic(sk21,sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi13,h1066]) ).
cnf(h1112,plain,
cong(sk21,sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi43,h1083,h1057,h1057,h37]) ).
cnf(h1164,plain,
midp(sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi67,h1112,h51]) ).
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(h1176,plain,
midp(sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi64,h1164,h30,h30]) ).
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(h1193,plain,
midp(sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi45,h1176,h698,h48]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h1262,plain,
cong(sk20,sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi68,h1193]) ).
cnf(h640,plain,
para(sk21,sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi4,h38]) ).
cnf(h1178,plain,
midp(sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi45,h1164,h640,h42]) ).
cnf(h1223,plain,
cong(sk20,sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi68,h1178]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
ifeq(cong(X0,X1,X2,X3),true,ifeq(cong(X2,X3,X4,X5),true,cong(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h1731,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi24,h1223,h1262]) ).
cnf(h2598,plain,
midp(sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi67,h1731,h23]) ).
cnf(h2650,plain,
midp(sk20,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi64,h2598,h30,h30]) ).
cnf(h2715,plain,
midp(sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi45,h2650,h38,h40]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD63) ).
fof(f63_nnf,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [M,A,B,C,D] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( para(X0,X2,X1,X3)
| ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi63,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X0,X3,X4),true,para(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(h3508,plain,
para(sk21,sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi63,h2715,h3411]) ).
cnf(h5378,plain,
midp(sk23,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi45,h2715,h3508,h181]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h5671,plain,
midp(sk23,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi10,h5378]) ).
cnf(h6575,plain,
midp(sk24,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi45,h5671,h583,h160]) ).
cnf(t29,plain,
cong(sk24,sk23,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi68,h6575]) ).
cnf(t1266,plain,
cong(sk24,sk23,sk24,sk20) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(c118,plain,
~ cong(sk24,sk23,sk24,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cong(sk24,sk23,sk24,sk20) != true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1266]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO578+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 12:27:26 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.61/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.61/1.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------