%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ANA125^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Wed Oct 7 10:09:42 AM UTC 2026
% Result : Theorem 0.08s 0.21s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA125^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.15 % Computer : n013.cluster.edu
% 0.08/0.15 % Model : x86_64 x86_64
% 0.08/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.15 % Memory : 8046.5625MB
% 0.08/0.15 % OS : Linux 6.8.0-71-generic
% 0.08/0.15 % CPULimit : 300
% 0.08/0.15 % WCLimit : 300
% 0.08/0.15 % DateTime : Tue Oct 6 18:18:53 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.21
% 0.08/0.21 No.of.Axioms: 2
% 0.08/0.21
% 0.08/0.21 Length.of.Defs: 0
% 0.08/0.21
% 0.08/0.21 Contains.Choice.Funs: false
% 0.08/0.21 eprover: <stdin>:1:(Column 43):(just read ''const/iterate/polynomial_function''): Closing bracket (')') expected, but String enclosed in single quote ('') read
% 0.08/0.21 eprover: <stdin>:1:(Column 43):(just read ''const/iterate/polynomial_function''): Closing bracket (')') expected, but String enclosed in single quote ('') read
% 0.08/0.21 .eprover: <stdin>:1:(Column 43):(just read ''const/iterate/polynomial_function''): Closing bracket (')') expected, but String enclosed in single quote ('') read
% 0.08/0.21 .
% 0.08/0.21
% 0.08/0.21 ********************************
% 0.08/0.21 * All subproblems solved! *
% 0.08/0.21 ********************************
% 0.08/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:94,loop_count:12,foatp_calls:3,translation:fof_experiment)
% 0.08/0.21
% 0.08/0.21 %**** Beginning of derivation protocol ****
% 0.08/0.21 % SZS output start CNFRefutation
% 0.08/0.21 thf(tp_'type/realax/real',type,('type/realax/real': $tType)).
% 0.08/0.21 thf(tp_'const/iterate/polynomial_function',type,('const/iterate/polynomial_function': (('type/realax/real'>'type/realax/real')>$o))).
% 0.08/0.21 thf(tp_'const/realax/real_mul',type,('const/realax/real_mul': ('type/realax/real'>('type/realax/real'>'type/realax/real')))).
% 0.08/0.21 thf(tp_sK1_A,type,(sK1_A: ('type/realax/real'>'type/realax/real'))).
% 0.08/0.21 thf(tp_sK2_SY8,type,(sK2_SY8: 'type/realax/real')).
% 0.08/0.21 thf(tp_sK3_E,type,(sK3_E: 'type/realax/real')).
% 0.08/0.21 thf(tp_sK4_E,type,(sK4_E: 'type/realax/real')).
% 0.08/0.21 thf(tp_sK5_E,type,(sK5_E: (('type/realax/real'>'type/realax/real')>('type/realax/real'>'type/realax/real')))).
% 0.08/0.21 thf(tp_sK6_E,type,(sK6_E: 'type/realax/real')).
% 0.08/0.21 thf(tp_sK7_E,type,(sK7_E: 'type/realax/real')).
% 0.08/0.21 thf(tp_sK8_E,type,(sK8_E: ('type/realax/real'>'type/realax/real'))).
% 0.08/0.21 thf(1,axiom,(![A:'type/realax/real',A0:'type/realax/real']: ((('const/realax/real_mul'@A)@A0) = (('const/realax/real_mul'@A0)@A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_MUL_SYM_')).
% 0.08/0.21 thf(2,axiom,(![A:('type/realax/real'>'type/realax/real'),A0:'type/realax/real']: (('const/iterate/polynomial_function'@A) => ('const/iterate/polynomial_function'@(^[A1:'type/realax/real']: (('const/realax/real_mul'@A0)@(A@A1)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_')).
% 0.08/0.21 thf(3,conjecture,(![A:('type/realax/real'>'type/realax/real'),A0:'type/realax/real']: (('const/iterate/polynomial_function'@A) => ('const/iterate/polynomial_function'@(^[A1:'type/realax/real']: (('const/realax/real_mul'@(A@A1))@A0))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_RMUL_')).
% 0.08/0.21 thf(4,negated_conjecture,(((![A:('type/realax/real'>'type/realax/real'),A0:'type/realax/real']: (('const/iterate/polynomial_function'@A) => ('const/iterate/polynomial_function'@(^[A1:'type/realax/real']: (('const/realax/real_mul'@(A@A1))@A0)))))=$false)),inference(negate_conjecture,[status(cth)],[3])).
% 0.08/0.21 thf(5,plain,(((![A:('type/realax/real'>'type/realax/real'),A0:'type/realax/real']: (('const/iterate/polynomial_function'@A) => ('const/iterate/polynomial_function'@(^[A1:'type/realax/real']: (('const/realax/real_mul'@(A@A1))@A0)))))=$false)),inference(unfold_def,[status(thm)],[4])).
% 0.08/0.21 thf(6,plain,(((![A:'type/realax/real',A0:'type/realax/real']: ((('const/realax/real_mul'@A)@A0) = (('const/realax/real_mul'@A0)@A)))=$true)),inference(unfold_def,[status(thm)],[1])).
% 0.08/0.21 thf(7,plain,(((![A:('type/realax/real'>'type/realax/real'),A0:'type/realax/real']: (('const/iterate/polynomial_function'@A) => ('const/iterate/polynomial_function'@(^[A1:'type/realax/real']: (('const/realax/real_mul'@A0)@(A@A1))))))=$true)),inference(unfold_def,[status(thm)],[2])).
% 0.08/0.21 thf(8,plain,(((![SY8:'type/realax/real']: (('const/iterate/polynomial_function'@sK1_A) => ('const/iterate/polynomial_function'@(^[SY9:'type/realax/real']: (('const/realax/real_mul'@(sK1_A@SY9))@SY8)))))=$false)),inference(extcnf_forall_neg,[status(esa)],[5])).
% 0.08/0.21 thf(9,plain,(((('const/iterate/polynomial_function'@sK1_A) => ('const/iterate/polynomial_function'@(^[SY10:'type/realax/real']: (('const/realax/real_mul'@(sK1_A@SY10))@sK2_SY8))))=$false)),inference(extcnf_forall_neg,[status(esa)],[8])).
% 0.08/0.21 thf(10,plain,((('const/iterate/polynomial_function'@sK1_A)=$true)),inference(standard_cnf,[status(thm)],[9])).
% 0.08/0.21 thf(11,plain,((('const/iterate/polynomial_function'@(^[SY10:'type/realax/real']: (('const/realax/real_mul'@(sK1_A@SY10))@sK2_SY8)))=$false)),inference(standard_cnf,[status(thm)],[9])).
% 0.08/0.21 thf(12,plain,(((~ ('const/iterate/polynomial_function'@(^[SY10:'type/realax/real']: (('const/realax/real_mul'@(sK1_A@SY10))@sK2_SY8))))=$true)),inference(polarity_switch,[status(thm)],[11])).
% 0.08/0.21 thf(13,plain,(((![A:('type/realax/real'>'type/realax/real')]: ((~ ('const/iterate/polynomial_function'@A)) | (![A0:'type/realax/real']: ('const/iterate/polynomial_function'@(^[A1:'type/realax/real']: (('const/realax/real_mul'@A0)@(A@A1)))))))=$true)),inference(extcnf_combined,[status(esa)],[7])).
% 0.08/0.21 thf(14,plain,(((![A:('type/realax/real'>'type/realax/real')]: ((~ ('const/iterate/polynomial_function'@A)) | (![A0:'type/realax/real']: ('const/iterate/polynomial_function'@(^[A1:'type/realax/real']: (('const/realax/real_mul'@A0)@(A@A1)))))))=$true)),inference(copy,[status(thm)],[13])).
% 0.08/0.21 thf(15,plain,(((![A:'type/realax/real',A0:'type/realax/real']: ((('const/realax/real_mul'@A)@A0) = (('const/realax/real_mul'@A0)@A)))=$true)),inference(copy,[status(thm)],[6])).
% 0.08/0.21 thf(16,plain,((('const/iterate/polynomial_function'@sK1_A)=$true)),inference(copy,[status(thm)],[10])).
% 0.08/0.21 thf(17,plain,(((~ ('const/iterate/polynomial_function'@(^[SY10:'type/realax/real']: (('const/realax/real_mul'@(sK1_A@SY10))@sK2_SY8))))=$true)),inference(copy,[status(thm)],[12])).
% 0.08/0.21 thf(18,plain,(![SV1:('type/realax/real'>'type/realax/real')]: ((((~ ('const/iterate/polynomial_function'@SV1)) | (![SY11:'type/realax/real']: ('const/iterate/polynomial_function'@(^[SY12:'type/realax/real']: (('const/realax/real_mul'@SY11)@(SV1@SY12))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[14])).
% 0.08/0.21 thf(19,plain,(![SV2:'type/realax/real']: (((![SY13:'type/realax/real']: ((('const/realax/real_mul'@SV2)@SY13) = (('const/realax/real_mul'@SY13)@SV2)))=$true))),inference(extcnf_forall_pos,[status(thm)],[15])).
% 0.08/0.21 thf(20,plain,((('const/iterate/polynomial_function'@(^[SY10:'type/realax/real']: (('const/realax/real_mul'@(sK1_A@SY10))@sK2_SY8)))=$false)),inference(extcnf_not_pos,[status(thm)],[17])).
% 0.08/0.21 thf(21,plain,(![SV1:('type/realax/real'>'type/realax/real')]: (((~ ('const/iterate/polynomial_function'@SV1))=$true) | ((![SY11:'type/realax/real']: ('const/iterate/polynomial_function'@(^[SY12:'type/realax/real']: (('const/realax/real_mul'@SY11)@(SV1@SY12)))))=$true))),inference(extcnf_or_pos,[status(thm)],[18])).
% 0.08/0.21 thf(22,plain,(![SV3:'type/realax/real',SV2:'type/realax/real']: ((((('const/realax/real_mul'@SV2)@SV3) = (('const/realax/real_mul'@SV3)@SV2))=$true))),inference(extcnf_forall_pos,[status(thm)],[19])).
% 0.08/0.21 thf(23,plain,(![SV1:('type/realax/real'>'type/realax/real')]: ((('const/iterate/polynomial_function'@SV1)=$false) | ((![SY11:'type/realax/real']: ('const/iterate/polynomial_function'@(^[SY12:'type/realax/real']: (('const/realax/real_mul'@SY11)@(SV1@SY12)))))=$true))),inference(extcnf_not_pos,[status(thm)],[21])).
% 0.08/0.21 thf(24,plain,(![SV1:('type/realax/real'>'type/realax/real'),SV4:'type/realax/real']: ((('const/iterate/polynomial_function'@(^[SY14:'type/realax/real']: (('const/realax/real_mul'@SV4)@(SV1@SY14))))=$true) | (('const/iterate/polynomial_function'@SV1)=$false))),inference(extcnf_forall_pos,[status(thm)],[23])).
% 0.08/0.21 thf(27,plain,(![SV5:'type/realax/real',SV6:'type/realax/real']: ((((('const/realax/real_mul'@SV6)@SV5) = (('const/realax/real_mul'@SV5)@SV6))=$true))),inference(rename,[status(thm)],[22])).
% 0.08/0.21 thf(35,plain,(![SV7:('type/realax/real'>'type/realax/real'),SV8:'type/realax/real']: ((('const/iterate/polynomial_function'@(^[SX0:'type/realax/real']: (('const/realax/real_mul'@SV8)@(SV7@SX0))))=$true) | (('const/iterate/polynomial_function'@SV7)=$false))),inference(rename,[status(thm)],[24])).
% 0.08/0.21 thf(41,plain,(![SV7:('type/realax/real'>'type/realax/real'),SV8:'type/realax/real']: (((('const/iterate/polynomial_function'@SV7) = ('const/iterate/polynomial_function'@sK1_A))=$false) | (('const/iterate/polynomial_function'@(^[SX0:'type/realax/real']: (('const/realax/real_mul'@SV8)@(SV7@SX0))))=$true))),inference(res,[status(thm)],[35,16])).
% 0.08/0.21 thf(42,plain,(![SV8:'type/realax/real']: ((('const/iterate/polynomial_function'@(^[SX0:'type/realax/real']: (('const/realax/real_mul'@SV8)@(sK1_A@SX0))))=$true))),inference(extuni,[status(esa)],[41:[bind(SV7,$thf(sK1_A))]])).
% 0.08/0.21 thf(51,plain,(![SV9:'type/realax/real']: ((('const/iterate/polynomial_function'@(^[SX0:'type/realax/real']: (('const/realax/real_mul'@SV9)@(sK1_A@SX0))))=$true))),inference(rename,[status(thm)],[42])).
% 0.08/0.21 thf(55,plain,(![SV9:'type/realax/real']: (((('const/iterate/polynomial_function'@(^[SX0:'type/realax/real']: (('const/realax/real_mul'@SV9)@(sK1_A@SX0)))) = ('const/iterate/polynomial_function'@(^[SY10:'type/realax/real']: (('const/realax/real_mul'@(sK1_A@SY10))@sK2_SY8))))=$false))),inference(res,[status(thm)],[51,20])).
% 0.08/0.21 thf(56,plain,(![SV9:'type/realax/real']: ((((('const/realax/real_mul'@SV9)@(sK1_A@(sK8_E@SV9))) = (('const/realax/real_mul'@(sK1_A@(sK8_E@SV9)))@sK2_SY8))=$false))),inference(extuni,[status(esa)],[55])).
% 0.08/0.21 thf(89,plain,(![SV12:'type/realax/real']: ((((('const/realax/real_mul'@SV12)@(sK1_A@(sK8_E@SV12))) = (('const/realax/real_mul'@(sK1_A@(sK8_E@SV12)))@sK2_SY8))=$false))),inference(rename,[status(thm)],[56])).
% 0.08/0.21 thf(92,plain,(![SV12:'type/realax/real',SV5:'type/realax/real',SV6:'type/realax/real']: (((((('const/realax/real_mul'@SV12)@(sK1_A@(sK8_E@SV12))) = (('const/realax/real_mul'@(sK1_A@(sK8_E@SV12)))@sK2_SY8)) = ((('const/realax/real_mul'@SV6)@SV5) = (('const/realax/real_mul'@SV5)@SV6)))=$false))),inference(res,[status(thm)],[89,27])).
% 0.08/0.21 thf(94,plain,((($false)=$true)),inference(extuni,[status(esa)],[92:[bind(SV12,$thf(sK2_SY8)),bind(SV5,$thf(sK2_SY8)),bind(SV6,$thf(sK1_A@(sK8_E@sK2_SY8)))]])).
% 0.08/0.21 thf(95,plain,($false),inference(solved_all_splits,[solved_all_splits(join,[])],[94])).
% 0.08/0.21 % SZS output end CNFRefutation
% 0.08/0.21
% 0.08/0.21 %**** End of derivation protocol ****
% 0.08/0.21 %**** no. of clauses in derivation: 35 ****
% 0.08/0.21 %**** clause counter: 94 ****
% 0.08/0.21
% 0.08/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:94,loop_count:12,foatp_calls:3,translation:fof_experiment)
%------------------------------------------------------------------------------