%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV011+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Wed Jul 20 17:49:41 EDT 2022 % Result : Theorem 3.68s 1.50s % Output : Proof 4.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV011+1 : TPTP v8.1.0. Released v2.4.0. % 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Wed Jun 15 07:19:52 EDT 2022 % 0.19/0.34 % CPUTime : % 0.57/0.59 ____ _ % 0.57/0.59 ___ / __ \_____(_)___ ________ __________ % 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.59 % 0.57/0.59 A Theorem Prover for First-Order Logic % 0.57/0.60 (ePrincess v.1.0) % 0.57/0.60 % 0.57/0.60 (c) Philipp Rümmer, 2009-2015 % 0.57/0.60 (c) Peter Backeman, 2014-2015 % 0.57/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.60 Bug reports to peter@backeman.se % 0.57/0.60 % 0.57/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.60 % 0.57/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.42/0.90 Prover 0: Preprocessing ... % 1.72/1.02 Prover 0: Warning: ignoring some quantifiers % 1.72/1.04 Prover 0: Constructing countermodel ... % 2.95/1.36 Prover 0: gave up % 2.95/1.36 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.95/1.38 Prover 1: Preprocessing ... % 3.26/1.44 Prover 1: Constructing countermodel ... % 3.53/1.50 Prover 1: proved (139ms) % 3.68/1.50 % 3.68/1.50 No countermodel exists, formula is valid % 3.68/1.50 % SZS status Theorem for theBenchmark % 3.68/1.50 % 3.68/1.50 Generating proof ... found it (size 17) % 4.49/1.74 % 4.49/1.74 % SZS output start Proof for theBenchmark % 4.49/1.74 Assumed formulas after preprocessing and simplification: % 4.49/1.74 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (a_stored(v3) = 0 & fresh_to_b(an_a_nonce) = 0 & t_holds(v6) = 0 & t_holds(v5) = 0 & party_of_protocol(b) = 0 & party_of_protocol(a) = 0 & party_of_protocol(t) = 0 & generate_key(an_a_nonce) = v7 & generate_expiration_time(an_a_nonce) = v9 & generate_b_nonce(an_a_nonce) = v12 & pair(v11, v13) = v14 & pair(b, an_a_nonce) = v3 & pair(a, an_a_nonce) = v1 & quadruple(b, an_a_nonce, v7, v9) = v17 & encrypt(v21, bt) = v22 & encrypt(v17, at) = v18 & encrypt(v12, v7) = v13 & encrypt(v10, bt) = v11 & triple(v18, v11, v12) = v19 & triple(b, v12, v22) = v23 & triple(a, v7, v9) = v10 & triple(a, an_a_nonce, v9) = v21 & sent(b, t, v23) = v24 & sent(a, b, v14) = v15 & sent(a, b, v1) = v2 & sent(t, a, v19) = v20 & message(v24) = 0 & message(v20) = 0 & message(v15) = 0 & message(v2) = 0 & b_stored(v1) = 0 & a_holds(v16) = 0 & a_holds(v0) = 0 & key(v7, b) = v16 & key(v7, a) = v8 & key(bt, b) = v6 & key(bt, t) = v4 & key(at, a) = v5 & key(at, t) = v0 & b_holds(v8) = 0 & b_holds(v4) = 0 & ! [v25] : ! [v26] : ! [v27] : ! [v28] : ! [v29] : ! [v30] : (v26 = v25 | ~ (quadruple(v30, v29, v28, v27) = v26) | ~ (quadruple(v30, v29, v28, v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : ! [v28] : ! [v29] : (v26 = v25 | ~ (triple(v29, v28, v27) = v26) | ~ (triple(v29, v28, v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : ! [v28] : ! [v29] : (v26 = v25 | ~ (sent(v29, v28, v27) = v26) | ~ (sent(v29, v28, v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : ! [v28] : (v26 = v25 | ~ (pair(v28, v27) = v26) | ~ (pair(v28, v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : ! [v28] : (v26 = v25 | ~ (encrypt(v28, v27) = v26) | ~ (encrypt(v28, v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : ! [v28] : (v26 = v25 | ~ (key(v28, v27) = v26) | ~ (key(v28, v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (a_stored(v27) = v26) | ~ (a_stored(v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (fresh_to_b(v27) = v26) | ~ (fresh_to_b(v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (t_holds(v27) = v26) | ~ (t_holds(v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (party_of_protocol(v27) = v26) | ~ (party_of_protocol(v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (generate_key(v27) = v26) | ~ (generate_key(v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (generate_expiration_time(v27) = v26) | ~ (generate_expiration_time(v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (generate_b_nonce(v27) = v26) | ~ (generate_b_nonce(v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (message(v27) = v26) | ~ (message(v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (b_stored(v27) = v26) | ~ (b_stored(v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (a_holds(v27) = v26) | ~ (a_holds(v27) = v25)) & ! [v25] : ! [v26] : ! [v27] : (v26 = v25 | ~ (b_holds(v27) = v26) | ~ (b_holds(v27) = v25)) & ! [v25] : ! [v26] : ( ~ (key(v25, b) = v26) | ? [v27] : ? [v28] : ? [v29] : (a_holds(v26) = v27 & key(v25, a) = v28 & b_holds(v28) = v29 & ( ~ (v29 = 0) | ~ (v27 = 0))))) % 4.49/1.78 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23, all_0_24_24 yields: % 4.49/1.78 | (1) a_stored(all_0_21_21) = 0 & fresh_to_b(an_a_nonce) = 0 & t_holds(all_0_18_18) = 0 & t_holds(all_0_19_19) = 0 & party_of_protocol(b) = 0 & party_of_protocol(a) = 0 & party_of_protocol(t) = 0 & generate_key(an_a_nonce) = all_0_17_17 & generate_expiration_time(an_a_nonce) = all_0_15_15 & generate_b_nonce(an_a_nonce) = all_0_12_12 & pair(all_0_13_13, all_0_11_11) = all_0_10_10 & pair(b, an_a_nonce) = all_0_21_21 & pair(a, an_a_nonce) = all_0_23_23 & quadruple(b, an_a_nonce, all_0_17_17, all_0_15_15) = all_0_7_7 & encrypt(all_0_3_3, bt) = all_0_2_2 & encrypt(all_0_7_7, at) = all_0_6_6 & encrypt(all_0_12_12, all_0_17_17) = all_0_11_11 & encrypt(all_0_14_14, bt) = all_0_13_13 & triple(all_0_6_6, all_0_13_13, all_0_12_12) = all_0_5_5 & triple(b, all_0_12_12, all_0_2_2) = all_0_1_1 & triple(a, all_0_17_17, all_0_15_15) = all_0_14_14 & triple(a, an_a_nonce, all_0_15_15) = all_0_3_3 & sent(b, t, all_0_1_1) = all_0_0_0 & sent(a, b, all_0_10_10) = all_0_9_9 & sent(a, b, all_0_23_23) = all_0_22_22 & sent(t, a, all_0_5_5) = all_0_4_4 & message(all_0_0_0) = 0 & message(all_0_4_4) = 0 & message(all_0_9_9) = 0 & message(all_0_22_22) = 0 & b_stored(all_0_23_23) = 0 & a_holds(all_0_8_8) = 0 & a_holds(all_0_24_24) = 0 & key(all_0_17_17, b) = all_0_8_8 & key(all_0_17_17, a) = all_0_16_16 & key(bt, b) = all_0_18_18 & key(bt, t) = all_0_20_20 & key(at, a) = all_0_19_19 & key(at, t) = all_0_24_24 & b_holds(all_0_16_16) = 0 & b_holds(all_0_20_20) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (quadruple(v5, v4, v3, v2) = v1) | ~ (quadruple(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (sent(v4, v3, v2) = v1) | ~ (sent(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (encrypt(v3, v2) = v1) | ~ (encrypt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (key(v3, v2) = v1) | ~ (key(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (a_stored(v2) = v1) | ~ (a_stored(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (fresh_to_b(v2) = v1) | ~ (fresh_to_b(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (t_holds(v2) = v1) | ~ (t_holds(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (party_of_protocol(v2) = v1) | ~ (party_of_protocol(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (generate_key(v2) = v1) | ~ (generate_key(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (generate_expiration_time(v2) = v1) | ~ (generate_expiration_time(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (generate_b_nonce(v2) = v1) | ~ (generate_b_nonce(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (message(v2) = v1) | ~ (message(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (b_stored(v2) = v1) | ~ (b_stored(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (a_holds(v2) = v1) | ~ (a_holds(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (b_holds(v2) = v1) | ~ (b_holds(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (key(v0, b) = v1) | ? [v2] : ? [v3] : ? [v4] : (a_holds(v1) = v2 & key(v0, a) = v3 & b_holds(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) % 4.79/1.79 | % 4.79/1.79 | Applying alpha-rule on (1) yields: % 4.79/1.79 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (sent(v4, v3, v2) = v1) | ~ (sent(v4, v3, v2) = v0)) % 4.79/1.79 | (3) pair(a, an_a_nonce) = all_0_23_23 % 4.79/1.79 | (4) encrypt(all_0_12_12, all_0_17_17) = all_0_11_11 % 4.79/1.79 | (5) key(bt, t) = all_0_20_20 % 4.79/1.79 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (quadruple(v5, v4, v3, v2) = v1) | ~ (quadruple(v5, v4, v3, v2) = v0)) % 4.79/1.79 | (7) key(bt, b) = all_0_18_18 % 4.79/1.79 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (generate_expiration_time(v2) = v1) | ~ (generate_expiration_time(v2) = v0)) % 4.79/1.79 | (9) encrypt(all_0_7_7, at) = all_0_6_6 % 4.79/1.79 | (10) generate_expiration_time(an_a_nonce) = all_0_15_15 % 4.79/1.79 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (generate_b_nonce(v2) = v1) | ~ (generate_b_nonce(v2) = v0)) % 4.79/1.79 | (12) message(all_0_4_4) = 0 % 4.79/1.79 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (t_holds(v2) = v1) | ~ (t_holds(v2) = v0)) % 4.79/1.79 | (14) triple(a, all_0_17_17, all_0_15_15) = all_0_14_14 % 4.79/1.79 | (15) party_of_protocol(t) = 0 % 4.79/1.79 | (16) b_holds(all_0_16_16) = 0 % 4.79/1.79 | (17) generate_key(an_a_nonce) = all_0_17_17 % 4.79/1.79 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (generate_key(v2) = v1) | ~ (generate_key(v2) = v0)) % 4.79/1.79 | (19) encrypt(all_0_14_14, bt) = all_0_13_13 % 4.79/1.79 | (20) ! [v0] : ! [v1] : ( ~ (key(v0, b) = v1) | ? [v2] : ? [v3] : ? [v4] : (a_holds(v1) = v2 & key(v0, a) = v3 & b_holds(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) % 4.79/1.79 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (b_stored(v2) = v1) | ~ (b_stored(v2) = v0)) % 4.79/1.79 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (a_stored(v2) = v1) | ~ (a_stored(v2) = v0)) % 4.79/1.79 | (23) triple(all_0_6_6, all_0_13_13, all_0_12_12) = all_0_5_5 % 4.79/1.79 | (24) party_of_protocol(a) = 0 % 4.79/1.79 | (25) key(at, a) = all_0_19_19 % 4.79/1.79 | (26) triple(b, all_0_12_12, all_0_2_2) = all_0_1_1 % 4.79/1.79 | (27) sent(t, a, all_0_5_5) = all_0_4_4 % 4.79/1.79 | (28) t_holds(all_0_18_18) = 0 % 4.79/1.79 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (key(v3, v2) = v1) | ~ (key(v3, v2) = v0)) % 4.79/1.79 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (a_holds(v2) = v1) | ~ (a_holds(v2) = v0)) % 4.79/1.79 | (31) a_holds(all_0_8_8) = 0 % 4.79/1.79 | (32) sent(a, b, all_0_23_23) = all_0_22_22 % 4.79/1.79 | (33) t_holds(all_0_19_19) = 0 % 4.79/1.79 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (party_of_protocol(v2) = v1) | ~ (party_of_protocol(v2) = v0)) % 4.79/1.79 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (b_holds(v2) = v1) | ~ (b_holds(v2) = v0)) % 4.79/1.79 | (36) fresh_to_b(an_a_nonce) = 0 % 4.79/1.79 | (37) generate_b_nonce(an_a_nonce) = all_0_12_12 % 4.79/1.79 | (38) message(all_0_0_0) = 0 % 4.79/1.79 | (39) key(all_0_17_17, a) = all_0_16_16 % 4.79/1.79 | (40) a_stored(all_0_21_21) = 0 % 4.79/1.79 | (41) message(all_0_22_22) = 0 % 4.79/1.79 | (42) encrypt(all_0_3_3, bt) = all_0_2_2 % 4.79/1.79 | (43) b_stored(all_0_23_23) = 0 % 4.79/1.79 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (fresh_to_b(v2) = v1) | ~ (fresh_to_b(v2) = v0)) % 4.79/1.80 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) % 4.79/1.80 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (message(v2) = v1) | ~ (message(v2) = v0)) % 4.79/1.80 | (47) triple(a, an_a_nonce, all_0_15_15) = all_0_3_3 % 4.79/1.80 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) % 4.79/1.80 | (49) b_holds(all_0_20_20) = 0 % 4.79/1.80 | (50) sent(a, b, all_0_10_10) = all_0_9_9 % 4.79/1.80 | (51) party_of_protocol(b) = 0 % 4.79/1.80 | (52) key(all_0_17_17, b) = all_0_8_8 % 4.79/1.80 | (53) pair(b, an_a_nonce) = all_0_21_21 % 4.79/1.80 | (54) pair(all_0_13_13, all_0_11_11) = all_0_10_10 % 4.79/1.80 | (55) a_holds(all_0_24_24) = 0 % 4.79/1.80 | (56) key(at, t) = all_0_24_24 % 4.79/1.80 | (57) message(all_0_9_9) = 0 % 4.79/1.80 | (58) sent(b, t, all_0_1_1) = all_0_0_0 % 4.79/1.80 | (59) quadruple(b, an_a_nonce, all_0_17_17, all_0_15_15) = all_0_7_7 % 4.79/1.80 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (encrypt(v3, v2) = v1) | ~ (encrypt(v3, v2) = v0)) % 4.79/1.80 | % 4.79/1.80 | Instantiating formula (20) with all_0_8_8, all_0_17_17 and discharging atoms key(all_0_17_17, b) = all_0_8_8, yields: % 4.79/1.80 | (61) ? [v0] : ? [v1] : ? [v2] : (a_holds(all_0_8_8) = v0 & key(all_0_17_17, a) = v1 & b_holds(v1) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0))) % 4.87/1.80 | % 4.87/1.80 | Instantiating (61) with all_10_0_28, all_10_1_29, all_10_2_30 yields: % 4.87/1.80 | (62) a_holds(all_0_8_8) = all_10_2_30 & key(all_0_17_17, a) = all_10_1_29 & b_holds(all_10_1_29) = all_10_0_28 & ( ~ (all_10_0_28 = 0) | ~ (all_10_2_30 = 0)) % 4.87/1.80 | % 4.87/1.80 | Applying alpha-rule on (62) yields: % 4.87/1.80 | (63) a_holds(all_0_8_8) = all_10_2_30 % 4.87/1.80 | (64) key(all_0_17_17, a) = all_10_1_29 % 4.87/1.80 | (65) b_holds(all_10_1_29) = all_10_0_28 % 4.87/1.80 | (66) ~ (all_10_0_28 = 0) | ~ (all_10_2_30 = 0) % 4.87/1.80 | % 4.87/1.80 | Instantiating formula (30) with all_0_8_8, all_10_2_30, 0 and discharging atoms a_holds(all_0_8_8) = all_10_2_30, a_holds(all_0_8_8) = 0, yields: % 4.87/1.80 | (67) all_10_2_30 = 0 % 4.87/1.80 | % 4.87/1.80 | Instantiating formula (29) with all_0_17_17, a, all_10_1_29, all_0_16_16 and discharging atoms key(all_0_17_17, a) = all_10_1_29, key(all_0_17_17, a) = all_0_16_16, yields: % 4.87/1.80 | (68) all_10_1_29 = all_0_16_16 % 4.87/1.80 | % 4.87/1.80 | Instantiating formula (35) with all_0_16_16, all_10_0_28, 0 and discharging atoms b_holds(all_0_16_16) = 0, yields: % 4.87/1.80 | (69) all_10_0_28 = 0 | ~ (b_holds(all_0_16_16) = all_10_0_28) % 4.87/1.80 | % 4.87/1.80 | From (68) and (65) follows: % 4.87/1.80 | (70) b_holds(all_0_16_16) = all_10_0_28 % 4.87/1.80 | % 4.87/1.80 +-Applying beta-rule and splitting (69), into two cases. % 4.87/1.80 |-Branch one: % 4.87/1.80 | (71) ~ (b_holds(all_0_16_16) = all_10_0_28) % 4.87/1.80 | % 4.87/1.80 | Using (70) and (71) yields: % 4.87/1.81 | (72) $false % 4.87/1.81 | % 4.87/1.81 |-The branch is then unsatisfiable % 4.87/1.81 |-Branch two: % 4.87/1.81 | (70) b_holds(all_0_16_16) = all_10_0_28 % 4.87/1.81 | (74) all_10_0_28 = 0 % 4.87/1.81 | % 4.87/1.81 +-Applying beta-rule and splitting (66), into two cases. % 4.87/1.81 |-Branch one: % 4.87/1.81 | (75) ~ (all_10_0_28 = 0) % 4.87/1.81 | % 4.87/1.81 | Equations (74) can reduce 75 to: % 4.87/1.81 | (76) $false % 4.87/1.81 | % 4.87/1.81 |-The branch is then unsatisfiable % 4.87/1.81 |-Branch two: % 4.87/1.81 | (74) all_10_0_28 = 0 % 4.87/1.81 | (78) ~ (all_10_2_30 = 0) % 4.87/1.81 | % 4.87/1.81 | Equations (67) can reduce 78 to: % 4.87/1.81 | (76) $false % 4.87/1.81 | % 4.87/1.81 |-The branch is then unsatisfiable % 4.87/1.81 % SZS output end Proof for theBenchmark % 4.87/1.81 % 4.87/1.81 1202ms %------------------------------------------------------------------------------