%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO271+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 : Thu Sep 24 08:40:12 AM UTC 2026
% Result : Theorem 222.45s 222.72s
% Output : Proof 222.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO271+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 07:45:45 UTC 2026
% 0.11/0.36 % CPUTime :
% 222.45/222.72 % SZS status Theorem for theBenchmark
% 222.45/222.72 % SZS output start Proof for theBenchmark
% 222.45/222.72 fof(qu(theu(the(211), 1), imp(the(211))), conjecture,
% 222.45/222.72 ! [ Vdthex ] : ( ( ron(vd1057, Vdthex) & rcenter(vd1055, Vdthex) & rcircle(Vdthex) ) => Vdthex = vd1061 ),
% 222.45/222.72 file('theBenchmark.p', qu(theu(the(211), 1), imp(the(211)))) ).
% 222.45/222.72
% 222.45/222.72 fof(and(pred(comma_conjunct2(the(211)), 0), and(pred(comma_conjunct1(the(211)), 0), pred(the(211), 0))), axiom,
% 222.45/222.72 ( ron(vd1057, vd1061) & rcenter(vd1055, vd1061) & rcircle(vd1061) ),
% 222.45/222.72 file('theBenchmark.p', and(pred(comma_conjunct2(the(211)), 0), and(pred(comma_conjunct1(the(211)), 0), pred(the(211), 0)))) ).
% 222.45/222.72
% 222.45/222.72 fof(and(pred(conjunct2(210), 4), and(holds(conjunct2(210), 1059, 0), and(pred(conjunct2(210), 1), and(pred(conjunct1(210), 2), pred(conjunct1(210), 1))))), axiom,
% 222.45/222.72 ( vd1057 = vd1058 & ~( vd1055 = vd1057 ) & rpoint(vd1058) & vd1055 = vd1056 & rpoint(vd1056) ),
% 222.45/222.72 file('theBenchmark.p', and(pred(conjunct2(210), 4), and(holds(conjunct2(210), 1059, 0), and(pred(conjunct2(210), 1), and(pred(conjunct1(210), 2), pred(conjunct1(210), 1)))))) ).
% 222.45/222.72
% 222.45/222.72 fof(qu(cond(axiom(182), 0), imp(cond(axiom(182), 0))), axiom,
% 222.45/222.72 ! [ Vd837,Vd838,Vd842,Vd843,Vd844 ] : ( ( vf(Vd842, Vd837) = vf(Vd842, Vd838) & ron(Vd838, Vd844) & ron(Vd837, Vd843) & rcenter(Vd842, Vd844) & rcenter(Vd842, Vd843) & ? [ Vd841 ] : ( Vd838 = Vd841 & rpoint(Vd841) ) & ? [ Vd840 ] : ( Vd837 = Vd840 & rpoint(Vd840) ) ) => Vd843 = Vd844 ),
% 222.45/222.72 file('theBenchmark.p', qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))) ).
% 222.45/222.72
% 222.45/222.72 fof(f_1_1, negated_conjecture,
% 222.45/222.72 ~( ! [ Vdthex ] : ( ( ron(vd1057, Vdthex) & rcenter(vd1055, Vdthex) & rcircle(Vdthex) ) => Vdthex = vd1061 ) ),
% 222.45/222.72 inference(negate,[status(cth)],[qu(theu(the(211), 1), imp(the(211)))]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_1_2, negated_conjecture,
% 222.45/222.72 ? [ Vdthex ] : ( ( ron(vd1057, Vdthex) & rcenter(vd1055, Vdthex) & rcircle(Vdthex) ) & ~( Vdthex = vd1061 ) ),
% 222.45/222.72 inference(fof_nnf,[status(thm)],[f_1_1]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_1_3, negated_conjecture,
% 222.45/222.72 ? [ U_0 ] : ( ( ron(vd1057, U_0) & rcenter(vd1055, U_0) & rcircle(U_0) ) & ~( U_0 = vd1061 ) ),
% 222.45/222.72 inference(variable_rename,[status(thm)],[f_1_2]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_1_4, negated_conjecture,
% 222.45/222.72 ( ( ron(vd1057, sK1) & rcenter(vd1055, sK1) & rcircle(sK1) ) & ~( sK1 = vd1061 ) ),
% 222.45/222.72 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1)],[f_1_3]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_1_5, negated_conjecture,
% 222.45/222.72 ( ( ( ron(vd1057, sK1) ) ) & ( ( rcenter(vd1055, sK1) ) ) & ( ( rcircle(sK1) ) ) & ( ( sK1 != vd1061 ) ) ),
% 222.45/222.72 inference(definitional_conversion,[status(esa)],[f_1_4]) ).
% 222.45/222.72
% 222.45/222.72 cnf(f_1_6, negated_conjecture,
% 222.45/222.72 ( ron(vd1057, sK1) ),
% 222.45/222.72 inference(clausify,[status(thm)],[f_1_5]) ).
% 222.45/222.72
% 222.45/222.72 cnf(f_1_7, negated_conjecture,
% 222.45/222.72 ( rcenter(vd1055, sK1) ),
% 222.45/222.72 inference(clausify,[status(thm)],[f_1_5]) ).
% 222.45/222.72
% 222.45/222.72 cnf(f_1_9, negated_conjecture,
% 222.45/222.72 ( sK1 != vd1061 ),
% 222.45/222.72 inference(clausify,[status(thm)],[f_1_5]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_2_1, plain,
% 222.45/222.72 ( ron(vd1057, vd1061) & rcenter(vd1055, vd1061) & rcircle(vd1061) ),
% 222.45/222.72 inference(fof_nnf,[status(thm)],[and(pred(comma_conjunct2(the(211)), 0), and(pred(comma_conjunct1(the(211)), 0), pred(the(211), 0)))]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_2_2, plain,
% 222.45/222.72 ( ( ( ron(vd1057, vd1061) ) ) & ( ( rcenter(vd1055, vd1061) ) ) & ( ( rcircle(vd1061) ) ) ),
% 222.45/222.72 inference(definitional_conversion,[status(esa)],[f_2_1]) ).
% 222.45/222.72
% 222.45/222.72 cnf(f_2_3, plain,
% 222.45/222.72 ( ron(vd1057, vd1061) ),
% 222.45/222.72 inference(clausify,[status(thm)],[f_2_2]) ).
% 222.45/222.72
% 222.45/222.72 cnf(f_2_4, plain,
% 222.45/222.72 ( rcenter(vd1055, vd1061) ),
% 222.45/222.72 inference(clausify,[status(thm)],[f_2_2]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_3_1, plain,
% 222.45/222.72 ( vd1057 = vd1058 & ~( vd1055 = vd1057 ) & rpoint(vd1058) & vd1055 = vd1056 & rpoint(vd1056) ),
% 222.45/222.72 inference(fof_nnf,[status(thm)],[and(pred(conjunct2(210), 4), and(holds(conjunct2(210), 1059, 0), and(pred(conjunct2(210), 1), and(pred(conjunct1(210), 2), pred(conjunct1(210), 1)))))]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_3_2, plain,
% 222.45/222.72 ( ( ( vd1057 = vd1058 ) ) & ( ( vd1055 != vd1057 ) ) & ( ( rpoint(vd1058) ) ) & ( ( vd1055 = vd1056 ) ) & ( ( rpoint(vd1056) ) ) ),
% 222.45/222.72 inference(definitional_conversion,[status(esa)],[f_3_1]) ).
% 222.45/222.72
% 222.45/222.72 cnf(f_3_3, plain,
% 222.45/222.72 ( vd1057 = vd1058 ),
% 222.45/222.72 inference(clausify,[status(thm)],[f_3_2]) ).
% 222.45/222.72
% 222.45/222.72 cnf(f_3_5, plain,
% 222.45/222.72 ( rpoint(vd1058) ),
% 222.45/222.72 inference(clausify,[status(thm)],[f_3_2]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_15_1, plain,
% 222.45/222.72 ! [ Vd837,Vd838,Vd842,Vd843,Vd844 ] : ( ( ~( vf(Vd842, Vd837) = vf(Vd842, Vd838) ) | ~( ron(Vd838, Vd844) ) | ~( ron(Vd837, Vd843) ) | ~( rcenter(Vd842, Vd844) ) | ~( rcenter(Vd842, Vd843) ) | ! [ Vd841 ] : ( ~( Vd838 = Vd841 ) | ~( rpoint(Vd841) ) ) | ! [ Vd840 ] : ( ~( Vd837 = Vd840 ) | ~( rpoint(Vd840) ) ) ) | Vd843 = Vd844 ),
% 222.45/222.72 inference(fof_nnf,[status(thm)],[qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_15_2, plain,
% 222.45/222.72 ! [ U_141,U_140,U_139,U_138,U_137 ] : ( ( ~( vf(U_139, U_141) = vf(U_139, U_140) ) | ~( ron(U_140, U_137) ) | ~( ron(U_141, U_138) ) | ~( rcenter(U_139, U_137) ) | ~( rcenter(U_139, U_138) ) | ! [ U_135 ] : ( ~( U_140 = U_135 ) | ~( rpoint(U_135) ) ) | ! [ U_136 ] : ( ~( U_141 = U_136 ) | ~( rpoint(U_136) ) ) ) | U_138 = U_137 ),
% 222.45/222.72 inference(variable_rename,[status(thm)],[f_15_1]) ).
% 222.45/222.72
% 222.45/222.72 fof(f_15_3, plain,
% 222.45/222.72 ( ( ! [U_140, U_139, U_141, U_135, U_136, U_137, U_138] : ( vf(U_139, U_141) != vf(U_139, U_140) | ~ron(U_140, U_137) | ~ron(U_141, U_138) | ~rcenter(U_139, U_137) | ~rcenter(U_139, U_138) | U_140 != U_135 | ~rpoint(U_135) | U_141 != U_136 | ~rpoint(U_136) | U_138 = U_137 ) ) ),
% 222.45/222.72 inference(definitional_conversion,[status(esa)],[f_15_2]) ).
% 222.45/222.72
% 222.45/222.72 cnf(f_15_4, plain,
% 222.45/222.72 ( vf(U_139, U_141) != vf(U_139, U_140) | ~ron(U_140, U_137) | ~ron(U_141, U_138) | ~rcenter(U_139, U_137) | ~rcenter(U_139, U_138) | U_140 != U_135 | ~rpoint(U_135) | U_141 != U_136 | ~rpoint(U_136) | U_138 = U_137 ),
% 222.45/222.72 inference(clausify,[status(thm)],[f_15_3]) ).
% 222.45/222.72
% 222.45/222.72 cnf(equality_1, axiom,
% 222.45/222.72 ( Eq_x_0 = Eq_x_0 ),
% 222.45/222.72 theory(equality,[reflexivity]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t1, plain, ( sK1 != vd1061 ),
% 222.45/222.72 inference(start, [status(thm), parent(0:0)], [f_1_9]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t2, plain, ( sK1 = vd1061 | vd1057 != vd1058 | ~rcenter(vd1055, sK1) | vf(vd1055, vd1057) != vf(vd1055, vd1057) | ~rpoint(vd1058) | ~rcenter(vd1055, vd1061) | ~ron(vd1057, sK1) | ~rpoint(vd1058) | vd1057 != vd1058 | ~ron(vd1057, vd1061) ),
% 222.45/222.72 inference(extension, [status(thm), parent(t1:1)], [f_15_4]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t3, plain, $false,
% 222.45/222.72 inference(connection, [status(thm), parent(t2:1)], [t2:1,t1:1]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t4, plain, ( vd1057 = vd1058 ),
% 222.45/222.72 inference(extension, [status(thm), parent(t2:2)], [f_3_3]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t5, plain, $false,
% 222.45/222.72 inference(connection, [status(thm), parent(t4:1)], [t4:1,t2:2]) ).
% 222.45/222.72
% 222.45/222.72 cnf(l2, lemma, vd1057 = vd1058,
% 222.45/222.72 inference(lemma, [status(cth), parent(t2:2), below(t1:1)], [t2:2]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t6, plain, ( rcenter(vd1055, sK1) ),
% 222.45/222.72 inference(extension, [status(thm), parent(t2:3)], [f_1_7]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t7, plain, $false,
% 222.45/222.72 inference(connection, [status(thm), parent(t6:1)], [t6:1,t2:3]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t8, plain, ( vf(vd1055, vd1057) = vf(vd1055, vd1057) ),
% 222.45/222.72 inference(extension, [status(thm), parent(t2:4)], [equality_1]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t9, plain, $false,
% 222.45/222.72 inference(connection, [status(thm), parent(t8:1)], [t8:1,t2:4]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t10, plain, ( rpoint(vd1058) ),
% 222.45/222.72 inference(extension, [status(thm), parent(t2:5)], [f_3_5]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t11, plain, $false,
% 222.45/222.72 inference(connection, [status(thm), parent(t10:1)], [t10:1,t2:5]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t12, plain, ( rcenter(vd1055, vd1061) ),
% 222.45/222.72 inference(extension, [status(thm), parent(t2:6)], [f_2_4]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t13, plain, $false,
% 222.45/222.72 inference(connection, [status(thm), parent(t12:1)], [t12:1,t2:6]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t14, plain, ( ron(vd1057, sK1) ),
% 222.45/222.72 inference(extension, [status(thm), parent(t2:7)], [f_1_6]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t15, plain, $false,
% 222.45/222.72 inference(connection, [status(thm), parent(t14:1)], [t14:1,t2:7]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t16, plain, ( rpoint(vd1058) ),
% 222.45/222.72 inference(extension, [status(thm), parent(t2:8)], [f_3_5]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t17, plain, $false,
% 222.45/222.72 inference(connection, [status(thm), parent(t16:1)], [t16:1,t2:8]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t18, plain, vd1057 = vd1058,
% 222.45/222.72 inference(lemma_extension, [status(thm), parent(t2:9)], [l2:1]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t19, plain, $false,
% 222.45/222.72 inference(connection, [status(thm), parent(t18:1)], [t18:1,t2:9]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t20, plain, ( ron(vd1057, vd1061) ),
% 222.45/222.72 inference(extension, [status(thm), parent(t2:10)], [f_2_3]) ).
% 222.45/222.72
% 222.45/222.72 cnf(t21, plain, $false,
% 222.45/222.72 inference(connection, [status(thm), parent(t20:1)], [t20:1,t2:10]) ).
% 222.45/222.72
% 222.45/222.72 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------